Question

Suppose cosθ = 0.766 and 270° < θ < 360°. Find sinθ.

Answer 1

okay... first, is sin θ going to be positive or negative in that interval?

Answer 2

negative

Answer 3

Okay, good. So we can use this identity
\[\huge \cos^2\theta + \sin^2\theta = 1\]\[\huge \sin^2\theta = 1 - \cos^2 \theta\]

Answer 4

plug in for cos θ

Answer 5

and take the square root of both sides
\[\huge \sin \theta\]

Answer 6

\[\huge \sin \theta = -\sqrt{1-\cos^2 \theta}\]
(remember that sine would be negative)

Answer 7

so would \[\cos ^2\] be removed and replace with 0.766? or would it be 0.766^2?

Answer 8

0.766^2
:)
cos θ = 0.766
cos^2 θ = 0.766^2

Answer 9

oooh ok

Answer 10

Satisfied? :)

Answer 11

yep. is the answer -0.643? just to be sure?

Answer 12

Yes.

Answer 13

ok. Thank you :)

Answer 14

Good that you understood it :)
I have to go now.
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Terence out