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 = 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 = □ (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 formula for cosine

For a point \((x, y)\) on the terminal side of an angle \(\theta\), the radius \(r\) is given by \(r=\sqrt{x^{2}+y^{2}}\), and \(\cos\theta=\frac{x}{r}\).
Here, \(x = - 7\) and \(y = 24\). First, we find \(r\):
\(r=\sqrt{(-7)^{2}+24^{2}}=\sqrt{49 + 576}=\sqrt{625}=25\)

Step2: Calculate \(\cos\theta\)

Using the formula \(\cos\theta=\frac{x}{r}\), substitute \(x=-7\) and \(r = 25\):
\(\cos\theta=\frac{-7}{25}\)

Answer:

\(-\frac{7}{25}\)