Question

Find the values of the trigonometric functions of t from the given information. If sin(t) = -5/13 and the terminal point of t is in quadrant IV, what are the values of cos(t), tan(t), sec(t), csc(t), and cot(t)?

Answer 1

The values of the trigonometric functions of t when sin(t) = -5/13 and the terminal point of t is in quadrant IV, are cos(t) = 12/13, tan(t) = -5/12, sec(t) = 13/12, csc(t) = -13/5, and cot(t) = -12/5.

Step-by-step explanation:

Given that sin(t) = -5/13 and the terminal point of t is in quadrant IV, we can determine the values of the trigonometric functions of t as follows:

1. To find cos(t), we use the identity sin²(t) + cos²(t) = 1. Since sin(t) = -5/13, we have (-5/13)² + cos²(t) = 1. Solving for cos(t), we get cos(t) = 12/13.
2. To find tan(t), we use the identity tan(t) = sin(t)/cos(t). Substituting the known values, we get tan(t) = (-5/13)/(12/13) = -5/12.
3. To find sec(t), we use the identity sec(t) = 1/cos(t). Substituting the known value, we get sec(t) = 1/(12/13) = 13/12.
4. To find csc(t), we use the identity csc(t) = 1/sin(t). Substituting the known value, we get csc(t) = 1/(-5/13) = -13/5.
5. To find cot(t), we use the identity cot(t) = 1/tan(t). Substituting the known value, we get cot(t) = 1/(-5/12) = -12/5.