If cosθ = square root 2 over 2 and 3 pi over 2 < θ < 2π, what are the values of sinθ and tanθ?

Solution:

Given: cosθ = √2/2 and 3π/2 < θ < 2π

We know that

sin²θ + cos²θ = 1

Substituting the values

sin²θ + (√2/2)² = 1

By further calculation

sin²θ = 1 - 1/2

sin²θ = 1/2

So we get

sinθ = -√2/2 [As θ lies between 3π/2 < θ < 2π in IV quadrant]

tanθ = sinθ/cosθ

Substituting the values

tanθ = (-√2/2)/(√2/2)

By further calculation

tanθ = -1

Therefore, the values of sinθ and tanθ are -√2/2 and -1.

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If cosθ = square root 2 over 2 and 3 pi over 2 < θ < 2π, what are the values of sinθ and tanθ?

Summary:

If cosθ = square root 2 over 2 and 3 pi over 2 < θ < 2π, the values of sinθ and tanθ are -√2/2 and -1.