Help!! Math problem

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
user_786
@user_786 (1338)
•
13 Feb 09
I dont know the answer to these and looks like many mylotters , too are not good enough in Maths, maybe a little attempt by yourself can solve the problem and the extra bonus you will receive of being able to solve other such problems easily yourself
1 person likes this
masata
@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
lonely_f16
@lonely_f16 (2146)
• Philippines
14 Feb 09
what does K here mean?
masata
@masata (408)
• Indonesia
16 Feb 09
k is integer. It is related to the periodicity of trigonometric function. Sine and Cosine are periodic every 2*pi (360 degrees) whereas tangent are periodic every pi (180 degrees).
masata
@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
masata
@masata (408)
• Indonesia
13 Feb 09
sorry I miss pi in 13/12 and 17/12. It should be 13pi/12 and 17pi/12. Thanks.
limitbreaker
@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.