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July 11, 2014

Homework Help: trigonometry (please double check this)

Posted by anon on Thursday, March 3, 2011 at 6:32am.

Solve the following trig equations. give all the positive values of the angle between 0 degrees and 360 degrees that will satisfy each. give any approximate value to the nearest minute only.

1. sin2 = (sqrt 3)/2
2. sin^2 = cos^2 + 1/2
3. sin 2x - cosx = 0
4. cos 4x = sin 2x


(((* stands for degrees)))



q1
sin2 = (sqrt 3)/2
2 = sin^-1 (sqrt3/2)
= 60*, 120*, 420*, 480*
= 30*, 60*, 210* and 240*

(not sure of the rest)

q2
sin^2 = cos^2 + 1/2
sin^2 - cos^2 = 1/2 ...(1)

sin^2 + cos^2 = 1 ...(2)

(1) + (2),
2sin^2 = 3/2
sin^2 = 3/4
sin = +-3/2
= 60*, 120*, 240* and 300*

q3
sin 2x - cosx = 0
2sinxcosx - cosx = 0
cos x (2sin x - 1) = 0
cos x = 0 or sin x = 1/2
x = 90*, 270* or
x = 30* 150*

answer, x = 30*, 90*, 150* and 270*

q4
cos 4x = sin 2x
2(sin 2x)^2 + sin 2x - 1 = 0
(2sin 2x - 1)(sin 2x + 1) = 0
sin 2x = -1, 1/2
2x = 30*, 150*, 270*, 390*, 510*, 630*
x = 15*, 75*, 135*, 195*, 255* and 315*

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