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

Example Questions

Example Question #1 : Find The Value Of The Sine Or Cosine Functions Of An Angle Given A Point On Its Terminal Side

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 #2 : Find The Value Of The Sine Or Cosine Functions Of An Angle Given A Point On Its Terminal Side

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 #3 : Find The Value Of The Sine Or Cosine Functions Of An Angle Given A Point On Its Terminal Side

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