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Question

Let (-7,-5) be a point on the terminal side of 0.

Find the exact values of cos0, csc0, and tan0.

Answer 1

Answer 2

The point (-7, -5) is in quadrant III. It's simpler to calculate θ from the x-axis then add 180° to get the actual angle θ.

First calculate the radius r.

a² + b² = c² or a² + b² = r²

(-5)² + (-7)² = r²

r² = 74

r = √(74)

tanθ = (-5)/(-7) θ = tan^-1(-5)/(-7) = 35.54º

We add 180° to get our θ = 215.54º

Then calculate

tan(215.54) = 0.7143

cos(215.54) = -0.814

csc(215.54) = -1.72

However, we can also do it without the calculator.

We know tanθ = (-5)/(-7)

(r)cosθ = -7

cosθ = -7/r = -7/√(74)

(r)sinθ = -5

sinθ = -5/√(74)

cscθ = 1/sinθ = √(74)/-5