Question

sketch an angle θ in standard position such that θ has the least possible positive measure and the point (-3,4) 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. ⓐ sin θ = \\(\frac{4}{5}\\) (simplify your answer. type an integer or a fraction.) ⓑ the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. ⓐ cos θ = \\(\frac{-3}{5}\\) (simplify your answer. type an integer or a fraction.) ⓑ the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. ⓐ tan θ = (simplify your answer. type an integer or a fraction.) ⓑ the function is undefined.

Explanation:

Step1: Find the radius \( r \)

Given the point \((-3, 4)\) on the terminal side of \(\theta\), we use the formula \( r = \sqrt{x^2 + y^2} \), where \( x = -3 \) and \( y = 4 \).
\[
r = \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

Step2: Calculate \( \tan\theta \)

The tangent function is defined as \( \tan\theta = \frac{y}{x} \). Substituting \( x = -3 \) and \( y = 4 \):
\[
\tan\theta = \frac{4}{-3} = -\frac{4}{3}
\]

Answer:

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