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In the diagram below, we have \(\sin \angle RPQ = \frac{7}{25}\). What is \(\cos \angle RPS\)?

 Dec 7, 2018

Best Answer 

 #2
avatar+100564 
+1

RPQ is supplemental to RPS

And the sines of supplemental angles are equal

Thus...... sin RPQ = sin RPS = 7/25

 

And since RPS is obtuse, the cosine of this angle =  - sqrt[ 25^2 - 7^2 ] / 25 =

 

- sqrt [ 625 - 49 ] / 25 =

 

- sqrt [ 576] / 25 =

 

-24 / 25

 

 

cool cool cool

 Dec 7, 2018
 #1
avatar+18360 
+1

cos(180°-θ) = - cos θ            & sin(180°-θ) = sin θ

 

So cos of rps = - cos rpq

 

1-sin^2 = cos^2

1-(7/25)^2 = cos^2

.96 =cos ^2

cos = .96                            - cos = - .96   (-24/25)

 Dec 7, 2018
edited by Guest  Dec 7, 2018
 #2
avatar+100564 
+1
Best Answer

RPQ is supplemental to RPS

And the sines of supplemental angles are equal

Thus...... sin RPQ = sin RPS = 7/25

 

And since RPS is obtuse, the cosine of this angle =  - sqrt[ 25^2 - 7^2 ] / 25 =

 

- sqrt [ 625 - 49 ] / 25 =

 

- sqrt [ 576] / 25 =

 

-24 / 25

 

 

cool cool cool

CPhill Dec 7, 2018

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