0 ≤ θ ≤ π . Find the value of θ in radians. = -sqrt 3/2 Write your answer in simplified, rationalized form. Do not round. θ = ______

Identify Angle: Identify the angle where the value of cosine is -sqrt(3)/2. In the unit circle, cos(θ) = -sqrt(3)/2 corresponds to an angle in the second quadrant.Determine Reference Angle: Determine the reference angle in the first quadrant that has a cosine of sqrt(3)/2. The reference angle is π/6 because cos(π/6) = sqrt(3)/2.Find Second Quadrant Angle: Find the angle in the second quadrant that has the same reference angle. The angle in the second quadrant is π - π/6, which simplifies to 5π/6.Check Angle Range: Check if the angle is within the given range. 5π/6 is between 0 and π, so it's within the range.

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$0$ $\leq \theta \leq \pi$ . Find the value of $\theta$ in radians. $\newline$ $\theta = -\sqrt{3}/2$ $\newline$ Write your answer in simplified, rationalized form. Do not round. $\newline$ $\theta =$ ______

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Algebra 2

Inverses of sin, cos, and tan: radians

Full solution

0

\leq \theta \leq \pi

. Find the value of

\theta

in radians.

\newline

\theta = -\sqrt{3}/2

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

______

Identify Angle: Identify the angle where the value of cosine is $-\sqrt{3}/2$ . In the unit circle, $\cos(\theta) = -\sqrt{3}/2$ corresponds to an angle in the second quadrant.
Determine Reference Angle: Determine the reference angle in the first quadrant that has a cosine of $\sqrt{3}/2$ . The reference angle is $\pi/6$ because $\cos(\pi/6) = \sqrt{3}/2$ .
Find Second Quadrant Angle: Find the angle in the second quadrant that has the same reference angle. $\newline$ The angle in the second quadrant is $\pi - \frac{\pi}{6}$ , which simplifies to $\frac{5\pi}{6}$ .
Check Angle Range: Check if the angle is within the given range. $5\pi/6$ is between $0$ and $\pi$ , so it's within the range.