+0

# precal

+5
30
2

sin\left(cos^{-1}\left(\frac{x^2}{4-x^2}\right)\right)

Guest Mar 9, 2017
Sort:

#1
0

sin(cos^(-1)(x^2/(4 - x^2)))

Solve for x:
sqrt(1 - x^4/(4 - x^2)^2) = 0

Square both sides:
1 - x^4/(4 - x^2)^2 = 0

Bring 1 - x^4/(4 - x^2)^2 together using the common denominator (x^2 - 4)^2:
-(8 (x^2 - 2))/(x^2 - 4)^2 = 0

Divide both sides by -8:
(x^2 - 2)/(x^2 - 4)^2 = 0

Multiply both sides by (x^2 - 4)^2:
x^2 - 2 = 0

x^2 = 2

Take the square root of both sides:
Answer: |x = sqrt(2)         or          x = -sqrt(2)

Guest Mar 9, 2017
#2
+75352
0

$$sin\left(cos^{-1}\left(\frac{x^2}{4-x^2}\right)\right)$$

We are looking for the sin of an angle (theta) with a cosine of   x^2 / ( 4 - x^2).....so we have...

sin (theta)   =  √ [ 1 - cos^2 (theta) ] =  [ 1 - [ (x^2)/(4-x^2)]^2 ] =  √ [x^4 - 8x^2 + 16 - x^4] / (4 - x^2)   =

√ {16 - 8x^2) / (4- x^2)    =  √ [ 4 (4 - 2x^2) ] / (4 - x^2)   =  2√(4 - 2x^2) / (4 - x^2)

CPhill  Mar 9, 2017

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details