Questions: Determine the reference angle for θ = 25π/4. What is the angle of least nonnegative measure coterminal with θ? θC= (Type your answer in radians. Type an exact answer, using π as needed. Use integers or fractions for any

$Determine the reference angle for θ = 25π/4. What is the angle of least nonnegative measure coterminal with θ? θC= (Type your answer in radians. Type an exact answer, using π as needed. Use integers or fractions for any$

Transcript text: Determine the reference angle for $\theta=\frac{25 \pi}{4}$. What is the angle of least nonnegative measure coterminal with $\theta$ ? \[ \theta_{C}= \] (Type your answer in radians. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any

Solution

Solution Steps

To determine the reference angle for $\theta = \frac{25 \pi}{4}$, we need to first find an equivalent angle between $0$ and $2\pi$. This can be done by reducing $\theta$ modulo $2\pi$. Once we have the equivalent angle, we can determine the reference angle based on which quadrant the angle lies in.

To find the angle of least nonnegative measure coterminal with $\theta$, we again reduce $\theta$ modulo $2\pi$.

Step 1: Determine the Coterminal Angle

To find the angle of least nonnegative measure coterminal with $\theta = \frac{25\pi}{4}$, we reduce $\theta$ modulo $2\pi$: \[ \theta_C = \theta \mod 2\pi = 0.7854 \text{ radians} \]

Step 2: Determine the Reference Angle

The reference angle is the acute angle formed by the terminal side of $\theta_C$ and the x-axis. Since $\theta_C = 0.7854$ radians is already in the first quadrant: \[ \text{Reference Angle} = \theta_C = 0.7854 \text{ radians} \]