Question 136476: These are very confusing for me. Here are a couple, I hope to use these examples to help me solve the rest.
Solve for x,
a) 4cos^2(2x+90)=3, x is in the interval[0,360)
b) If cotx=-3, find the Q2 family member of x in degrees
c) 2sin1/2x=sqrt3 over the interval [0,2pie], keep angle in pie radians
d) 2cos^2x-sinx-1=0, hint, replace cos^2x with one of the pythagorean identities
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve for x,
a) 4cos^2(2x+90)=3, x is in the interval[0,360)
cos^2(2x+90) = 3/4
cos(2x+90) = +0.75 or -0.75
If cos(2x+90) = 0.75,
Take the inverse cosine to get:
2x+90 = 41.4096 or 2x+90 = -41.4096
Then x = -24.295 degrees or x = -65.7048 degrees
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If cos(2x+90) = -0.75
Take the inverse cosine to get two values in the 2nd and 3rd quadrant
Then solve for x.
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b) If cotx=-3, find the Q2 family member of x in degrees
If cotx = -3, tanx= (-1/3)
Take the inverse tan to get:
x = -18.4349
The corresponding angle in Q2 is 180-18.4349 = 161.565. degrees
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c) 2sin1/2x=sqrt3 over the interval [0,2pie], keep angle in pie radians
sin(x/2) = (sqrt3)/2
Take the inverse sin of (sqrt3)/2 to get:
x/2 = 1.047197.. radians
x = 2.094395... radians
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d) 2cos^2x-sinx-1=0, hint, replace cos^2x with one of the pythagorean identities
2(1-sin^2x) - sinx -1 = 0
-2sin^2x -sinx +1 = 0
2sin^2x + sinx -1 = 0
Factor to get:
(2sinx-1)(sinx+1)=0
sinx = 1/2 or sinx = -1
x = 30 or 150 degrees
x = 270 degrees
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Cheers,
Stan H.
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