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Given the reference angle of (4pi)/(9), find the corresponding angle in Quadrant 4. Answer:

Given the reference angle of 4π9 \frac{4 \pi}{9} , find the corresponding angle in Quadrant 44.\newlineAnswer:

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Full solution

Q. Given the reference angle of 4π9 \frac{4 \pi}{9} , find the corresponding angle in Quadrant 44.\newlineAnswer:
  1. Understand concept reference angles quadrants: Understand the concept of reference angles and quadrants.\newlineA reference angle is the acute angle formed by the terminal side of an angle and the x-axis. Quadrant 44 is the region where the x-values are positive and the y-values are negative. To find the corresponding angle in Quadrant 44, we need to subtract the reference angle from 2π2\pi, since angles in Quadrant 44 have measures between π\pi and 2π2\pi.
  2. Calculate corresponding angle Quadrant 44: Calculate the corresponding angle in Quadrant 44.\newlineThe corresponding angle in Quadrant 44, θ\theta, can be found using the formula θ=2π−reference angle\theta = 2\pi - \text{reference angle}. Here, the reference angle is 4π9\frac{4\pi}{9}. So, θ=2π−4π9\theta = 2\pi - \frac{4\pi}{9}.
  3. Perform subtraction find exact value: Perform the subtraction to find the exact value of θ\theta.θ=2π−4π9=18π9−4π9=14π9\theta = 2\pi - \frac{4\pi}{9} = \frac{18\pi}{9} - \frac{4\pi}{9} = \frac{14\pi}{9}

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