Question 305065: If X is an acute angle and sin X= 1/2, then cos X= ? What is the answer and how do I get it? I'm taking accuplacer on Monday hopeful to avoid having to take intermediate algebra over the summer. Thanks to all for all your help, Mike
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If X is an acute angle and sin X= 1/2, then cos X= ? What is the answer and how do I get it? I'm taking accuplacer on Monday hopeful to avoid having to take intermediate algebra over the summer. Thanks to all for all your help, Mike------------------------
Trig ratios are written in two of three variables: x, y, and r
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They are related in the following way: r^2 = x^2 + y^2
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Your Problem:
Since sin(x) = 1/2, y = 1 and r = 2
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Therefore x = sqrt(2^2-1^2) = sqrt(3)
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So, cos(x) = x/r = sqrt(3)/2
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Comment: So, given any of the six trig ratios you can figure out
the other five. You just have to keep straight in your head how
the signs change in the different quadrants.
By that I mean, sin(x) may be 1/2 is the 2nd quadrant,
but cos(x) is -sqrt(3)/2 in the 2nd quadrant.
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Cheers,
Stan H.
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