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 showing a cardioide.

Cardioide

Illustration showing a cardioide.

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…

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle in the order in which they occur in the triangle. "The ten formulas used in the solution of spherical right triangles can be expressed by means of two rules, known as Napier's rules of circular parts."

Napier's Right Spherical Triangle

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle…

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle and the angles opposite.

Relationships In A Spherical Triangle

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle…

Illustration used, with the law of cosines, to find the relation between the three sides and an angle of a spherical triangle.

Relationships In A Spherical Triangle

Illustration used, with the law of cosines, to find the relation between the three sides and an angle…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case both angles b and c are greater than 90°.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case angle b<90&deg; and angle c>90&deg;.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration of a right spherical triangle with a and b the sides, and &alpha; and &beta; the angles opposite them. Side c is the hypotenuse.

Right Spherical Triangle

Illustration of a right spherical triangle with a and b the sides, and α and β the angles…

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as is the ground. This drawing could be used for shadow, proportion, trigonometric, or Pythagorean Theorem problems.

Palm Tree Perpendicular to Ground

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as…