A student claims that a given point is located in Quadrant III. The x-coordinate is −5
, and the cos(θ)
of the angle is −513
. Use a unit circle to complete the table with numbers that support the student's claim. Enter your answer in the table.

In the third quadrant, both the sine and the cosine are negative. The sine of the angle can be found from your knowledge of the {5, 12, 13} Pythagorean triple, or using the Pythagorean trig identity:

sin(θ) = -√(1 -cos(θ)²)

sin(θ) = -√(1 -(-5/13)²) = -√(144/169)

sin(θ) = -12/13

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A student claims that a given point is located in Quadrant III. The x-coordinate is −5 , and the cos(θ) of the angle is −513 . Use a unit circle to complete the table with numbers that support the student's claim. Enter your answer in the table.

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3rd Quadrant

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A student claims that a given point is located in Quadrant III. The x-coordinate is −5
, and the cos(θ)
of the angle is −513
. Use a unit circle to complete the table with numbers that support the student's claim. Enter your answer in the table.