Use a calculator to solve the equation on the interval 0 $0 \leq \theta

Question

Use a calculator to solve the equation on the interval 0 $0 \leq \theta < 2 \pi$ . Round the answer to two decimal places.
-$\sin \theta = - 0.41$
A) 3.56, 5.86
B) 0.42, 3.56
C) 0.42, 1.99
D) 0.42, 5.86

Quizplus · Accepted Answer

To solve $\sin \theta = -0.41$ for $0 \leq \theta < 2\pi$, first find the angle whose sine is -0.41. Using a calculator, $\theta \approx \arcsin(-0.41) \approx -0.42$ radians. Since the sine function is negative in the third and fourth quadrants, we find the equivalent positive angles in these quadrants. The third quadrant angle is $\pi - (-0.42) = 3.56$ radians, and the fourth quadrant angle is $2\pi - (-0.42) = 5.86$ radians, both rounded to two decimal places.

Use a Calculator to Solve the Equation on the Interval 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π

Use a Calculator to Solve the Equation on the Interval $0 \leq \theta < 2 \pi$