SOLUTION: Which value of x solves the equation cos x° = sin (20° + x°), where
0 < x < 90?
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Question 804624: Which value of x solves the equation cos x° = sin (20° + x°), where
0 < x < 90?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Which value of x solves the equation cos x° = sin (20° + x°), where
0 < x < 90?
--------------------
cos(x) = sin(90 - x)
----
sin(90 - x) = sin(20 + x)
90 - x = 20 + x
2x = 70
x = 35 degs
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
As we work this, keep in mind that sine and cosine are both positive in the first quadrant.
Use the formula for sine of the sum of two angles:
\ =\ \sin\alpha\cos\beta\ +\ \cos\alpha\sin\beta)
So
\ =\ \sin20^\circ\cos x^\circ\ +\ \cos20^\circ\sin x^\circ)
Hence we have:
A little algebra music, Sammy:
\ =\ \cos20^\circ\sin x^\circ)
But since sine over cosine is tangent:
)
The rest is just calculator work.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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