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. (-4,3) sinθ = 3/5 (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 = -4/5 (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 = (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 a point \((x,y)\) is on the terminal side, is given by \(\tan\theta=\frac{y}{x}\).

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

For the point \((-4,3)\), we have \(x = - 4\) and \(y=3\).

Step3: Calculate \(\tan\theta\)

Using the formula \(\tan\theta=\frac{y}{x}\), substitute \(x=-4\) and \(y = 3\) into it. So \(\tan\theta=\frac{3}{-4}=-\frac{3}{4}\).

Answer:

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