# Help!! Math problem

By lonely_f16

@lonely_f16 (2146)

Philippines

February 12, 2009 4:24pm CST

~Solve for the unique acute angle that satisfies the following,
x=arccos(1/2sinx)
~Find all solutions between 90 and 270 to
sin (5x-80 degrees) = square root of 3 divided by 2
~Find all solutions between 0 and 2 pie. to the ff conditional relationship.
2sin (2x) cos (3x) = cos (3x)
thanks a lot

4 responses

@masata (408)

• Indonesia

13 Feb 09

Second problem, I have the following solution.
sin(5x - 80) = sqrt(3) / 2
5x - 80 = 60 + k.360 or 5x - 80 = 120 + k.360, for k = .......,-2,-1,0,1,2,.....
5x = 140 + k.360 or 5x = 200 + k.360
x = 28 + k.72 or x = 40 + k.72
Solution must be between 90 and 270.
x = 100, 172, 244, 112, 184, 256

@masata (408)

• Indonesia

13 Feb 09

Third problem solution is as follows.
2sin(2x)cos(3x) = cos(3x)
cos(3x)*(2sin(2x) - 1) = 0
The equation requires either cos(3x) = 0 or 2sin(2x) - 1 = 0 or both.
First condition
cos(3x) = 0
3x = pi/2 + k.pi, for k = .....,-2,-1,0,1,2,........
x = pi/6 + k.pi/3
Plug in the values of k but they need to satisfy that 0

@limitbreaker (253)

• Philippines

13 Feb 09

cos x = 1/2 sin x
cos x / sinx = 1/2
sin x / cos x = 2
tan x = 2 ; x = arctan 2
sin (5x - 80) = sqrt 3 / 2
but sin 60 = sqrt 3 / 2
and sin 60 = sin 120
sin (5x - 80) = sin 120
5x - 80 = 120
5x = 120 + 80
(5x)/5 = 200/5
x = 40
2sin (2x) cos (3x) = cos (3x)
2sin 2x = 1
sin (2x) = 1/2
but sin 30 = 1/2
sin 2x = sin 30
2x = 30
x = 15
;sin 150 = 1/2
sin 2x = 150
2x = 150
x = 75
I hope my answers are correct.