$ ext{Determine the Quadrant of a Trigonometric Function}$
Answer 1
Abigail Nelson
Consider the angle $\theta = 210^\circ$. To determine the quadrant where this angle lies, we will use the unit circle.
The angle $210^\circ$ is measured from the positive x-axis in the counter-clockwise direction. Since $210^\circ > 180^\circ$ and $210^\circ < 270^\circ$, it lies in the third quadrant.
In the third quadrant, both sine and cosine values are negative. Therefore, the angle $\theta = 210^\circ$ lies in Quadrant III.
Answer 2
Ella Lewis
We need to find the quadrant of the angle $ heta = frac{5pi}{3}$ radians. First, we convert this angle to degrees.
Using the conversion $ heta = frac{5pi}{3} imes frac{180^circ}{pi} = 300^circ$, we see that the angle $300^circ$ is being considered.
The angle $300^circ$ is between $270^circ$ and $360^circ$, so it lies in Quadrant IV.
In Quadrant IV, the sine value is negative and the cosine value is positive. Therefore, the angle $ heta = frac{5pi}{3}$ radians lies in Quadrant IV.
Answer 3
Michael Moore
Consider the angle $ heta = 135^circ$. To find which quadrant it lies in, we start from the positive x-axis and measure counter-clockwise.
The angle $135^circ$ is between $90^circ$ and $180^circ$, so it falls in the second quadrant.
In the second quadrant, sine values are positive and cosine values are negative. Thus, $ heta = 135^circ$ lies in Quadrant II.
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