SOLUTION: How do you solve this? And what type of math is it? For 0 (degree symbol) is less than x is less than 90 (degree symbol), how many solutions are there for the equation 2 sin x =

Algebra ->  Trigonometry-basics -> SOLUTION: How do you solve this? And what type of math is it? For 0 (degree symbol) is less than x is less than 90 (degree symbol), how many solutions are there for the equation 2 sin x =      Log On


   

Question 333055: How do you solve this? And what type of math is it?
For 0 (degree symbol) is less than x is less than 90 (degree symbol), how many solutions are there for the equation 2 sin x = cos x
Found 2 solutions by solver91311, jrfrunner:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Trigonometry.



Square both sides:



Use the Pythagorean Identity



A little algebra





Take the square root, considering only the positive root because
both and are positive on the interval .



Rationalize the denominator, just for tidiness sake:



Then use the inverse function to solve for



And finally a little calculator work, in degrees mode because of the nature of the interval given, and we get:



Check







Close enough.

John

My calculator said it, I believe it, that settles it

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
in mathematics, there are many ways to solve some problems.
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the domain 0%3Cx%3C90 puts you in the first quadrant, where x=positive, y =positive
--
solve for x
2%2Asin%28x%29+=+cos%28x%29
2+=+cos%28x%29%2Fsin%28x%29=cot%28x%29=1%2Ftan%28x%29 (divide both sides by sin(x)
tan%28x%29=1%2F2 (invert both sides of the equation)
x=arctan%281%2F2%29=26.565
since x=26.565 resides within the domain 0%3Cx%3C90 this is the answer