Question

the point given below is on the terminal side of an angle θ in standard position. find the exact value of each of the six trigonometric functions of θ (12, -9) sinθ = -\frac{3}{5} (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression ) cosθ = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression )

Explanation:

Step1: Calculate the radius \(r\)

For a point \((x,y)\) on the terminal side of an angle \(\theta\), \(r=\sqrt{x^{2}+y^{2}}\). Here \(x = 12\) and \(y=-9\), so \(r=\sqrt{12^{2}+(-9)^{2}}=\sqrt{144 + 81}=\sqrt{225}=15\).

Step2: Calculate \(\cos\theta\)

The formula for \(\cos\theta\) is \(\cos\theta=\frac{x}{r}\). Substituting \(x = 12\) and \(r = 15\), we get \(\cos\theta=\frac{12}{15}=\frac{4}{5}\).

Answer:

\(\frac{4}{5}\)