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 = - 3/5 (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression ) cosθ = 4/5 (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.) tanθ = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression )

Explanation:

Step1: Recall the formula for \(\tan\theta\)

The formula for \(\tan\theta=\frac{\sin\theta}{\cos\theta}\)

Step2: Substitute the values of \(\sin\theta\) and \(\cos\theta\)

Given \(\sin\theta =-\frac{3}{5}\) and \(\cos\theta=\frac{4}{5}\), then \(\tan\theta=\frac{-\frac{3}{5}}{\frac{4}{5}}\)

Step3: Simplify the expression

\(\tan\theta=\frac{- 3}{5}\times\frac{5}{4}=-\frac{3}{4}\)

Answer:

\(-\frac{3}{4}\)