# HiSET: Math : Sine

## Example Questions

### Example Question #1 : Sine

Evaluate  in terms of .

Explanation:

Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring .

The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so

We can set the lengths of the opposite and adjacent legs to and 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:

The sine of the angle is equal to the ratio of the length opposite leg to that of the hypotenuse, so

.

### Example Question #2 : Sine

Evaluate  in terms of .

Explanation:

Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring . The cosine is defined to be the ratio of the length of the adjacent side to that of the hypotenuse, so

We can set the lengths of the adjacent leg and the hypotenuse to and 3, respectively. By the Pythagorean Theorem, the length of the opposite leg is

The sine of the angle is equal to the ratio of the length of the opposite leg to that of the hypotenuse, so

.