Question

a point p(x,y) is shown on the unit circle corresponding to a real number t. find the values of the trigonometric functions at t. the point p is p(-7/25, -24/25). a. sin t = -24/25 (type an integer or a simplified fraction.) b. cos t = -7/25 (type an integer or a simplified fraction.) c. tan t = 24/7 (type an integer or a simplified fraction.) d. csc t = -25/24 (type an integer or a simplified fraction.) e. sec t = (type an integer or a simplified fraction.)

Explanation:

Step1: Recall secant - cosine relationship

The secant function is the reciprocal of the cosine function, i.e., $\sec t=\frac{1}{\cos t}$.

Step2: Substitute the value of cos t

Given $\cos t =-\frac{7}{25}$, then $\sec t=\frac{1}{-\frac{7}{25}}$.

Step3: Simplify the expression

$\frac{1}{-\frac{7}{25}}=-\frac{25}{7}$.

Answer:

$-\frac{25}{7}$