Question 517849: What are the remaining trigonometric functions of theta when sin theta= square root 3/2, cos theta < 0.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What are the remaining trigonometric functions of theta when sin theta= square root 3/2, cos theta < 0
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When sin x =√2/3, and cos<0, it means the reference angle is in quadrant II, where sin>0 and cos<0. You are working with a right triangle where the opposite side=√2 and the hypotenuse=3. Using the Pythagorean Theorem, adjacent side =√[(3^2)-(√2)^2]=√(9-2)=√7
Trig functions:
sin x = √2/3 (given)
cos x = √7/3
tan x = √2/√7=√14/7
csc x =3/√2=3√2/2
sec x =3/√7=3√7/7
cot x =√7/√2=√14/2
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