SOLUTION: given cos(2a)=-17/18 and
0<2a< pi/2
find exact values
of the six trigonometric functions.
Note: you cannot us decimals in your answer
Algebra.Com
Question 632146: given cos(2a)=-17/18 and
0<2a< pi/2
find exact values
of the six trigonometric functions.
Note: you cannot us decimals in your answer
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First thing to note is that since 
, a simple division operation shows that 
, forcing 
to be a first quadrant angle, hence all six basic trigonometric functions will be positive.
\ \equiv\ \cos^2(\varphi)\ -\ \sin^2(\varphi))
So
\ -\ \sin^2(a)\ =\ -\frac{17}{18})
Since we know that
\ +\ \sin^2(\varphi)\ \equiv\ 1)
\ =\ -\frac{17}{18})
And then a little algebra music, Sammy:
\ =\ \pm\frac{\sqrt{35}}{6})
From which we discard the negative root because of the interval analysis earlier to get:
\ =\ \frac{\sqrt{35}}{6})
And likewise:
\ -\ 1\ =\ -\frac{17}{18})
From which we get:
\ =\ \frac{1}{6})
Use the following identities to get the other four functions:
\ \equiv\ \frac{\sin(\varphi)}{\cos(\varphi)})
\ \equiv\ \frac{1}{\tan{\varphi})
\ \equiv\ \frac{1}{\cos{\varphi})
\ \equiv\ \frac{1}{\sin{\varphi})
John
My calculator said it, I believe it, that settles it
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