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"So he drove out the man; and he placed at the east of the garden of Eden the Cherubim, and the flame of a sword which turned every way, to keep the way of the tree of life." Genesis 3:24 ASV <p>Illustration of Adam and Eve as they are sent away from the Garden of Eden and the Tree of Life. Both are wearing animal skins and Adam is covering his face. Two angels, both holding swords, stand in front of a tree. A dog stands next to the angels.One angel points Adam and Eve away from the garden. The serpent is at Eve's feet with its mouth open. God is pictured looking down from the clouds. A small, oval image of Mary holding the baby Jesus is inset above Eve's head.

Adam and Eve are Punished and Cast Out of the Garden of Eden

"So he drove out the man; and he placed at the east of the garden of Eden the Cherubim, and the flame…

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of the sines and cosines of the angles.

Sum of 2 Acute Angles

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of…

"And Jehovah sent fiery serpents among the people, and they bit the people; and much people of Israel died. And the people came to Moses, and said, We have sinned, because we have spoken against Jehovah, and against thee; pray unto Jehovah, that he take away the serpents from us. And Moses prayed for the people. And Jehovah said unto Moses, Make thee a fiery serpent, and set it upon a standard: and it shall come to pass, that every one that is bitten, when he seeth it, shall live." Numbers 21:6-8 ASV <p>Illustration of Moses holding up the bronze serpent on the staff and all of the Israelites looking upon it to be healed. Numerous people lie in various states of disease. Snakes are on the ground, coiled around arms, and biting people. Moses is pictured with horns made of rays of light. Tents and mountains can be seen in the background.

The Brazen Serpent and the Healing of the Israelites

"And Jehovah sent fiery serpents among the people, and they bit the people; and much people of Israel…

Illustration of one possible outcome (no triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is less than the height (bsin&alpha;).

Ambiguous Case

Illustration of one possible outcome (no triangle occurs) when discussing the ambiguous case using the…

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is equal to the height (bsin&alpha;).

Ambiguous Case

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the…

Illustration of one possible outcome (2 triangles occur) when discussing the ambiguous case using the Law of Sines. In this case, side a is greater than the height (bsin&alpha;).

Ambiguous Case

Illustration of one possible outcome (2 triangles occur) when discussing the ambiguous case using the…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. The circle is divided into four quadrants by the x- and y- axes. The circle can be labeled and used to find the six trigonometric values (sin, cos, tan, cot, sec, csc, cot) at each of the quadrantal angles.

Unit Circle

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. The…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in radian measure in terms of pi.

Unit Circle Labeled At Quadrantal Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles and angles that have reference angles of 30&deg;, 45&deg;, and 60&deg; are given in radian measure in terms of pi. At each quadrantal angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles and angles that have reference angles of 30&deg;, 45&deg;, and 60&deg; are given in radian measure in terms of pi.

Unit Circle Labeled At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 30&deg; increments, the angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 30° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees in 45&deg; increments. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45 ° Increments

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 45&deg; increments, the angles are given in both radian and degree measure. At each quadrantal angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 45&deg; increments, the angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All quadrantal angles are given in radian measure in terms of pi. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. At each quadrantal angle, the coordinates are given, but not the angle measure. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. At each…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At each quadrantal angle, the coordinates are given, but not the angle measure. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in radians. All quadrantal angles and angles that have reference angles of 30&deg;, 45&deg;, and 60&deg; are given in radian measure in terms of pi. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees at all quadrantal angles and angles that have reference angles of 30&deg;, 45&deg;, and 60&deg;. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees at all quadrantal angles and angles that have reference angles of 30&deg;, 45&deg;, and 60&deg;. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All quadrantal angles and angles that have reference angles of 30&deg;, 45&deg;, and 60&deg; are marked from the origin, but no values are given.

Unit Circle Marked At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All…

"They took Jesus therefore: and he went out, bearing the cross for himself, unto the place called The place of a skull, which is called in Hebrew, Golgotha..." John 19:17 ASV <p>Illustration of Jesus bearing his cross as his mother, Mary, falls to her knees in front of him. A disciple stands in the background (right). Simon stands behind Jesus with his left hand on the cross and a length of rope in his raised right hand. Behind Simon is another man, carrying a ladder. A crowd is following, including a soldier on a horse.

Jesus Carrying the Cross on the Way to Calvary

"They took Jesus therefore: and he went out, bearing the cross for himself, unto the place called The…

A curve that is a function and resembles the sine or cosine curve.

Trigonometric Curve

A curve that is a function and resembles the sine or cosine curve.

Illustration that can be used to show that when given an angle, expressed as an inverse function of u, it can be used to find the value of any function of the angle in terms of u.

Angle Expressed As An Inverse Function

Illustration that can be used to show that when given an angle, expressed as an inverse function of…

"And it came to pass, as soon as he came nigh unto the camp, that he saw the calf and the dancing: and Moses' anger waxed hot, and he cast the tables out of his hands, and brake them beneath the mount." Exodus 32:19 ASV <p>Illustration of Moses throwing down the stone tablets and breaking them after finding the Israelites worshiping an idol in the shape of a golden calf. One tablet lies broken on the ground and he is raising the second one, ready to smash it. Aaron stands next to him, distressed and trying to stop him. The people can be seen in the background, crowded around the golden calf. The tents are behind them.

Moses Breaks the Stone Tablets on Which the Ten Commandments are Written

"And it came to pass, as soon as he came nigh unto the camp, that he saw the calf and the dancing: and…

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and BD are perpendicular to OB and join B with C. The are of the triangle OBC is less than the are of the sector OBC, and the sector OBC is less than the triangle OBD.

Triangles and Sectors in Quadrant I

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and…

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Triangle in Quadrant I

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Triangle in Quadrant II

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Sine curve plotted from 0 to 2 pi. Graph of y=sin x.

Sine Curve y=sin x

Sine curve plotted from 0 to 2 pi. Graph of y=sin x.

Sine curves of varying frequency and amplitude plotted from 0 to 2 pi. Graph of y= sin &#952;, y= 1/2 sin &#952;, y=2 sin &#952;, y= 2 sin 3&#952;

Sine Curves y= sin Ǝ, y= 1/2 sin Ǝ, y=2 sin Ǝ, y= 2 sin 3Ǝ

Sine curves of varying frequency and amplitude plotted from 0 to 2 pi. Graph of y= sin θ, y= 1/2…

Sine curves of varying frequency plotted from 0 to 2 pi. Graph of y= sin t, y= r sin1/2t, y=r sin 2t.

Sine Curves y= sin t, y= r sin1/2t, y= r sin 2t

Sine curves of varying frequency plotted from 0 to 2 pi. Graph of y= sin t, y= r sin1/2t, y=r sin 2t.

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle any two sides are to each other as the sines of the opposite angles."

Law of Sines

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle…

A cartoon of a snake feeding a piece of cake to two children. A sign over the cake reads: The Forbidden Cake.

Snake Giving Two Children Cake

A cartoon of a snake feeding a piece of cake to two children. A sign over the cake reads: The Forbidden…

"The relief pictures an ancient Italian sacrifice of a bull, a ram, and a boar, offered to Mars to secure purification from sin. Note the sacred laurel trees, the two altars, and the officiating magistrate, whose head is covered with the toga. He is sprinkling incense from a box held by an attendant. Another attendant carries a ewer with the libation. In the rear is the sacrificer with his ax."&mdash;Webster, 1913

Suovetaurilia

"The relief pictures an ancient Italian sacrifice of a bull, a ram, and a boar, offered to Mars to secure…

"And with him they crucify two robbers; one on his right hand, and one on his left." Mark 15:27 ASV <p>Illustration of Jesus on the cross with a robber on his left and right. Mary Magdalene is at Jesus' feet. Jesus' mother, Mary, stands at the foot of the cross with another woman. Soldiers cast lots for Jesus' clothing (left). A soldier with a spear stands beside the cross.

The Crucifixion of Jesus with Two Robbers

"And with him they crucify two robbers; one on his right hand, and one on his left." Mark 15:27 ASV…

Illustration showing ambiguous case when the solution is not a triangle using law of sines.

Ambiguous Case of Law of Sines Triangle

Illustration showing ambiguous case when the solution is not a triangle using law of sines.

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric Reference Triangles/Angles (60 degrees) Drawn in Quadrants

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth horizontal plane.

Inclined Plane Forming Right Triangle

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth…

Triangle ABC and triangle ABC'. This illustration could be used to demonstrate the law of sines.

Triangles ABC and ABC'

Triangle ABC and triangle ABC'. This illustration could be used to demonstrate the law of sines.

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration could be used to find trig ratios.

Trigonometric Reference Triangles/Angles Drawn in Quadrants

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration…

"But when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her." John 8:7 ASV <p>Illustration of a woman kneeling at Jesus' feet. Several people stand around them. One man turns his face from the woman, while another turns his body away.

Jesus Tells a Crowd to Cast the First Stone

"But when they continued asking him, he lifted up himself, and said unto them, He that is without sin…

"And they, when they heard it, went out one by one, beginning from the eldest, even unto the last: and Jesus was left alone, and the woman, where she was, in the midst. And Jesus lifted up himself, and said unto her, Woman, where are they? did no man condemn thee? And she said, No man, Lord. And Jesus said, Neither do I condemn thee: go thy way; from henceforth sin no more." John 8:9-11 ASV <p>Illustration of Jesus standing next to two large columns. A woman is kneeling next to Jesus with her hands clasped.

Jesus Tells a Woman to Go and Sin No More

"And they, when they heard it, went out one by one, beginning from the eldest, even unto the last: and…