Find the values of the six trigonometric functions for each of the following indicated angles.

Question

I put the question here ---> https://webwhiteboard.com/board/o1wrs165utVRxVUqiwepLJsnfwHhMUvi/

Answer 1

Hi, Cyrene!

For this problem, the key is to identify which sides of the triangle are the hypotenuse, opposite, and adjacent sides relative to the indicated angle.

In this problem, the length of the hypotenuse (the side opposite of the right angle) is 25.

The side opposite the indicated angle T is length 24.

Finally, the side adjacent to the angle T is length z, and you correctly determined that z = 7.

Thus, we have H = 25, O = 24, and A = 7.

Now, all we have to do is plug these numbers into our SOH-CAH-TOA formulas.

SOH: sin(T) = O/H --> sin(T) = 24/25

CAH: cos(T) = A/H --> cos(T) = 7/25

TOA: tan(T) = O/A --> tan(T) = 24/7

Lastly, we can find csc(T), sec(T), and cot(T) by recalling that these functions are the reciprocals of sin(T), cos(T), and tan(T) respectively. Thus, all we have to do is flip the fractions that we have.

csc(T) = 1/sin(T) --> csc(T) = 25/24

sec(T) = 1/cos(T) --> sec(T) = 25/7

cot(T) = 1/tan(T) --> cot(T) = 7/24

I hope that this explanation is helpful, and please don't hesitate to reach out with any further questions!