Find the value for sin (θ) if the following conditions hold: cos (2 theta) = 3/4 and 270 degrees

Question

Carina Freeman

Mathematics

8 February, 13:43

Find the value for sin (θ) if the following conditions hold: cos (2 theta) = 3/4 and 270 degrees

+5

Answers (1)

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Alfredo Maynard · Answer 1

sin (θ) = - 0.35355

Step-by-step explanation:

The second condition is

270 degrees
cos (2*theta) = 3/4

And we know the relation

cos (2*θ) = 1-2sin^2 (θ)

This means that,

sin^2 (θ) = 0.5 * (1-cos (2*θ))

sin (θ) = ± √ (0.5 * (1-cos (2*θ)))

sin (θ) = ± √ (0.125)

sin (θ) = ± 0.35355

But we are in the 4th quadrant.

This means that the sine is negative.

sin (θ) = - 0.35355