sin? 0 = 1 – cos² 0 -1-() V3 =1 - 25 25 sin 0 = ± 20 sin 0 = The given expression of cosine is positive and tangent function is given to be less than 0, that is, negative, thus 0 must lie in quadrant IV. Now, take the negative value of the square root, because 0 is in quadrant IV and sine function is negative in quadrant IV. The value of sin 0, when cos (–Ø) tan 0 < 0, is – 2v3

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Analytic Trigonometry
Section7.2: Addition And Subtraction Formulas
Problem 69E
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How can you tell if theta lies in a certain quadrant when working with trigonometric identities?

I can solve the problem but I have a hard time knowing where theta lies and the concept behind it. 

please help

thank you 

sin? 0 = 1 – cos² 0
-1-()
V3
=1 -
25
25
sin 0 = ±
20
sin 0 =
The given expression of cosine is positive and tangent function is given
to be less than 0, that is, negative, thus 0 must lie in quadrant IV.
Now, take the negative value of the square root, because 0 is in quadrant
IV and sine function is negative in quadrant IV.
The value of sin 0, when cos (–Ø)
tan 0 < 0, is – 2v3
Transcribed Image Text:sin? 0 = 1 – cos² 0 -1-() V3 =1 - 25 25 sin 0 = ± 20 sin 0 = The given expression of cosine is positive and tangent function is given to be less than 0, that is, negative, thus 0 must lie in quadrant IV. Now, take the negative value of the square root, because 0 is in quadrant IV and sine function is negative in quadrant IV. The value of sin 0, when cos (–Ø) tan 0 < 0, is – 2v3
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