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 =
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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) (Show Source): You can put this solution on YOUR website!
Trigonometry.
\ =\ cos(x))
Square both sides:
\ =\ \cos^2(x))
Use the Pythagorean Identity \ +\ \sin^2(\varphi)\ =\ 1\text{ hence }\cos^2(\varphi)\ =\ 1\ -\ \sin^2(\varphi)\right))
\ =\ 1\ -\ \sin^2(x))
A little algebra
\ =\ 1)
\ =\ \frac{1}{5})
Take the square root, considering only the positive root because
both 
and 
are positive on the interval 
.
\ =\ \sqrt{\frac{1}{5}})
Rationalize the denominator, just for tidiness sake:
\ =\ \frac{sqrt{5}}{5})
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
\ \approx\ 0.448)
\ \approx\ 0.894)
Close enough.
John
My calculator said it, I believe it, that settles it
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
in mathematics, there are many ways to solve some problems.
---
the domain puts you in the first quadrant, where x=positive, y =positive
--
solve for x
(divide both sides by sin(x)
(invert both sides of the equation)
since x=26.565 resides within the domain this is the answer
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