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What is sin theta when sec theta = sqrt(5)?

 

 Aug 28, 2020
 #1
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secant: the reciprocal of a cosine

 

This just goes to say that the cosine of theta is 1/sqrt(5)

 

But...how does this help...at all? Well, you could just go and find the sin(arccos(1/sqrt(5)) and waste a lot of time trying, or you could use the fact that:

 

sin(theta)^2 + cos(theta)^2 = 1
 

With what we know, we can say this:

 

sin(theta)^2 + (1/sqrt(5))^2 = 1

sin(theta)^2 + 1/5 = 1

sin(theta)^2 = 4/5

sin(theta) = 2/sqrt(5)

 

Edit: oops, forgot to rationalize the denominator!


Multiply top and bottom by sqrt(5):

2sqrt(5)/5

 

:)

 Aug 28, 2020
edited by ilorty  Aug 28, 2020

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