Question

the point given below is on the terminal side of an angle θ. find the exact value of each of the six trigonometric functions of θ.
(-7,24)
sinθ = \frac{24}{25}
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)
cosθ = -\frac{7}{25}
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)
tanθ = \square
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Recall the definition of tangent

The tangent of an angle \(\theta\) in standard position, where the point \((x,y)\) is on the terminal side of \(\theta\), is given by \(\tan\theta=\frac{y}{x}\).

Step2: Identify \(x\) and \(y\) from the point

For the point \((-7,24)\), we have \(x = - 7\) and \(y=24\).

Step3: Calculate \(\tan\theta\)

Substitute \(x=-7\) and \(y = 24\) into the formula \(\tan\theta=\frac{y}{x}\). So \(\tan\theta=\frac{24}{-7}=-\frac{24}{7}\).

Answer:

\(-\frac{24}{7}\)