ClipArt ETC

This mathematics ClipArt gallery offers 9 illustrations of circles that are often used in trigonometry. Included are images showing arcs, angles, chords, and radians.

Illustration of Circle with radian shown.

Circle With Radian

Illustration of Circle with radian shown.

Circle with 36 degree angles marked. This diagram can be used with the following trig problem: Locate the centers of the holes B and C by finding the distance each is to the right and above the center O. The radius of the circle is 1.5 inches. Compute correct to three decimal places.

Circle With 36 degree Angles and Radius 1.5 in.

Circle with 36 degree angles marked. This diagram can be used with the following trig problem: Locate…

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height of the point P above the surface; it is required to find the distance from the point P to the horizon at A.

Circle With Center o and Radius r with point P

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height…

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle AOB, and the central angle AOB has the same measure as the arc AnB.

Circle With a Chord of 2 ft. and a Radius of 3 ft.

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle…

The coversedsine is equal to 1 minus the sine. In this figure, AE is parallel to OB; hence, EO = AC = sine of angle AOC, when radius OA - 1. Therefore, Coversedsine = 1 - sine = 1 - AC/OA = 1 - AC = 1 - EO = ER, when OA = 1.

Versedsine and Coversedsine in Circle

The coversedsine is equal to 1 minus the sine. In this figure, AE is parallel to OB; hence, EO = AC…

"If AOB is an angle of 1 ° on the larger circle, it is also 1 ° on the smaller concentric circle, and the length of the arc AB is to the length of the arc CD as to radius OB is to the radius OD; or, arc AB:arc CD = OB:OD."

Concentric Circles With Angle of 1 °

"If AOB is an angle of 1 ° on the larger circle, it is also 1 ° on the smaller concentric circle,…

Illustration showing that the radian is an angle that when placed at the center of a circle its sides intercept an arc equal to the radius.

Radians in Complete Circle

Illustration showing that the radian is an angle that when placed at the center of a circle its sides…

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." —Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

"In trigonometry, the arcs of circles are used to measure angles. All angles are supposed to have their vertexes at the center O of the circle, one side of the angle lying to the right of O, and coinciding with the horizontal diameter, as OB."

Arcs and Angles of a Trigonometric Circle

"In trigonometry, the arcs of circles are used to measure angles. All angles are supposed to have their…