Question

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.

Answer 1

sin(θ) = -12/13

Explanation:

You want the sine of the third-quadrant angle whose cosine is -5/13.

3rd Quadrant

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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