Question

sketch an angle θ in standard position such that θ has the least possible positive measure and the point (6,8) is on the terminal side of θ. then find the exact values of the six trigonometric functions for θ. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. sin θ = \\(\frac{4}{5}\\) (simplify your answer. type an integer or a fraction.) b. the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. cos θ = \\(\frac{3}{5}\\) (simplify your answer. type an integer or a fraction.) b. the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. tan θ = \\(\square\\) (simplify your answer. type an integer or a fraction.) b. the function is undefined.

Explanation:

Step1: Recall the formula for tangent

The tangent of an angle \(\theta\) in standard position with a point \((x,y)\) on its terminal side is given by \(\tan\theta=\frac{y}{x}\), where \(x
eq0\).

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

For the point \((6,8)\), we have \(x = 6\) and \(y = 8\).

Step3: Calculate \(\tan\theta\)

Substitute \(x = 6\) and \(y = 8\) into the formula: \(\tan\theta=\frac{8}{6}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \(\frac{8\div2}{6\div2}=\frac{4}{3}\).

Answer:

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