Question

Help please?

If sin O = -sqrt3 over 2 and n < O < 3 pi over 2, what are the values of cos O and tan O?​

Answer 1

• cos(θ) = -1/2
• tan(θ) = √3

Explanation:

You know that ...

• cos(θ)² = 1 - sin(θ)²
• tan(θ) = sin(θ)/cos(θ)
• cosine is negative in the third quadrant (where π < θ < 3π/2)

Using what you know about the relationships of these trig functions, you can find ...

cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4

cos(θ) = -1/2 . . . . . negative square root of 1/4

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tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)

tan(θ) = √3