SIN, COS, TAN question

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kalyan601

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"The angle θ is greater than 90◦ and less than 360◦ and cos θ =2/3. Find the exact value of tan θ."

So I have worked it out so far:
sin2 θ= 1- cos2 θ
since cos θ = 2/3
sin2 θ = 1- (2/3)2
sin2 θ= 5/9
sin θ= √5/3

sin θ/cos θ = tan θ
√5/3 / 2/3 = √5/2

However when looking through the mark scheme, the answer is negative and I do not understand why. The working marks are all exactly as I did except for the answer which should be negative although mine is not. Can some one tell me why?

 
Last edited:
kalyan601 said:
"The angle θ is greater than 90◦ and less than 360◦ and cos θ =2/3. Find the exact value of tan θ."

So I have worked it out so far:
sin2 θ= 1- cos2 θ
since cos θ = 2/3
sin2 θ = 1- (2/3)2
sin2 θ= 5/9
sin θ= ±√5/3.................... Here is the correction you need.

sin θ/cos θ = tan θ
√5/3 / 2/3 = √5/2

However when looking through the mark scheme, the answer is negative and I do not understand why. The working marks are all exactly as I did except for the answer which should be negative although mine is not. Can some one tell me why?
Click to expand...

You need to choose the negative value of sin(Θ) - because when 360°>Θ>90°, if cos(Θ)>0 → sin(Θ)<0 (in fourth quadrant).
 
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