Precalculus : Find the value of the sine or cosine functions of an angle given a point on its terminal side

Example Questions

Example Question #7 : Circular Functions

What is the sine of an angle if a point on the terminal side of the angle is ?      Explanation:

Given the point on the coordinate plane , the origin to this point can be computed by the Pythagorean Theorem.  The hypotenuse of the right triangle formed by the origin and the point is .

The length of the triangle is 1 unit, and the height of the triangle is 5.

Sine of an angle is opposite side divided by the hypotenuse. Rationalize the denominator. Example Question #1 : Circular Functions

Find the sine value of if it's a point on the terminal side of an angle in standard position.     Explanation:

This is a 30-60-90 triangle. A 30-60-90 triangle will have leg lengths of and 1 and a hypotenuse of 2. To find the sin value, you need to divide the opposite leg length with the hypotenuse (opposite/hypotenuse). Thus, giving you . Example Question #9 : Circular Functions

Find the secant value of if it's a point on the terminal side of an angle in standard position.     Explanation:

First, use the Pythagorean Theorem to solve for all the sides of the triangle. You know that the adjacent side is 4 units long, and the opposite side is -9 units long.

Using the Pythagorean Theorem, you should get a hypotenuse of . Secant is defined as hypotenuse/opposite.

Thus, giving you an answer of .

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