ClipArt ETC
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…

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 (bsinα).

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 (bsinα).

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 (bsinα).

Ambiguous Case

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

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate in either the second or fourth quadrant.

Negative Cotangent Angles

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate…

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…

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.

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…