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Find the exact value of sin(θ) for an angle θ with sec(θ) = 5/2 and with its terminal side in Quadrant IV.

 

 Apr 18, 2020
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Draw a picture!

 

It's in Quadrant IV, so the x-value (cos) will be positive and the y-value (sin) will be negative.

sec(theta)  =  5/2   --->   1/cos(theta)  =  5/2   --->   cos(theta)  =  2/5

 

In your reference triangle, the x-value  =  2  and the hypotenuse  =  5

Using the Pytagorean Theorem, the y-value  =  - sqrt(21)

 

sin  =  y / r   --->   sin(theta)  =  - sqrt(21) / 5

 

I think that the best way to approach these problems is to draw the picture ...

 Apr 18, 2020

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