Question

1. 0 / 1 points 6/15 submissions used find all angles θ between 0° and 180° that satisfy the given equation. round your answer(s) to one decimal place. (enter your answers as a comma - separated list. enter your answer in degrees.) tan(θ)=-25

Explanation:

Step1: Recall inverse - tangent property

We know that $\theta=\arctan(- 25)$. The range of the principal - value of $y = \arctan(x)$ is $(-90^{\circ},90^{\circ})$. Using a calculator, $\arctan(-25)\approx - 87.7^{\circ}$.

Step2: Find the angle in the given range

We want angles $\theta$ between $0^{\circ}$ and $180^{\circ}$. Since the tangent function has a period of $180^{\circ}$, and $\tan\theta=-25\lt0$, the tangent function is negative in the second quadrant. We can find the angle in the range $0^{\circ}$ to $180^{\circ}$ by adding $180^{\circ}$ to the principal - value of $\arctan(-25)$. So, $\theta\approx180^{\circ}+(-87.7^{\circ}) = 92.3^{\circ}$.

Answer:

$92.3^{\circ}$