Questions: Sketch an angle θ in standard position such that θ has the least possible positive measure and the point (-3,-4) is on the terminal side of 0 . 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= □ (Simplify your answer. Type an integer or fraction) B. The function is undefined.

$Sketch an angle θ in standard position such that θ has the least possible positive measure and the point (-3,-4) is on the terminal side of 0 . Then find the exact values of the six trigonometric functions for θ. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin θ= □ (Simplify your answer. Type an integer or fraction) B. The function is undefined.$

Transcript text: Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure and the point $(-3,-4)$ is on the terminal side of 0 . Then find the exact values of the six trigonometrie functions for $\theta$. Select the correct choice below and, if necessary, fill in the answer box to complete your cholice. A. $\sin \theta=$ $\square$ (Simplify your answer, Typto an intoger ore fremion) B. The function is undefined.

Solution

Solution Steps

Step 1: Identifying the correct graph

The point (-3, -4) lies in the third quadrant. The terminal side of the angle θ should pass through this point. Option B is the correct graph.

Step 2: Finding sin θ

The point on the terminal side is (-3, -4). This gives us x = -3 and y = -4. We can find the value of r using the Pythagorean theorem: $r = \sqrt{x^2 + y^2}$. $r = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

$\sin θ = \frac{y}{r} = \frac{-4}{5}$