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00 ≤θ≤π\leq \theta \leq \pi. Find the value of θ\theta in radians.\newlineθ=−3/2\theta = -\sqrt{3}/2\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ______

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Inverses of sin, cos, and tan: radiansright chevron icon

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Q. 00 ≤θ≤π\leq \theta \leq \pi. Find the value of θ\theta in radians.\newlineθ=−3/2\theta = -\sqrt{3}/2\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ______
  1. Identify Angle: Identify the angle where the value of cosine is −3/2-\sqrt{3}/2. In the unit circle, cos⁡(θ)=−3/2\cos(\theta) = -\sqrt{3}/2 corresponds to an angle in the second quadrant.
  2. Determine Reference Angle: Determine the reference angle in the first quadrant that has a cosine of 3/2\sqrt{3}/2. The reference angle is π/6\pi/6 because cos⁡(π/6)=3/2\cos(\pi/6) = \sqrt{3}/2.
  3. Find Second Quadrant Angle: Find the angle in the second quadrant that has the same reference angle.\newlineThe angle in the second quadrant is π−π6\pi - \frac{\pi}{6}, which simplifies to 5π6\frac{5\pi}{6}.
  4. Check Angle Range: Check if the angle is within the given range. 5π/65\pi/6 is between 00 and π\pi, so it's within the range.

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