Chapter 13.1, Problem 55HP

To determine

To explain whether the following statement is true or false.

Explanation of Solution

Given:

For any acute angle, the value of sine function is never negative.

Calculation:

True, since an acute angle means an angle whose measure is less than ${180}^{\circ }$ and in the first two quadrants the value of sine function is positive.

Hence, for any acute angle, the value of sine function is never negative.

There are defined values of sine function for each degree between 0 to 90. Further, for any degree more than 90 degree in the second quadrant the value can be calculated by subtracting that degree from 180 degree. The resulting degree lies between 0 to 90.