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July 31, 2014

Homework Help: trigonometry (please double check this)

Posted by anon on Thursday, March 3, 2011 at 5:34pm.

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.

a.)
( I got confused doing this 1 can you help me with it.)

3 sin theta - 4 cos theta = 2

b.)
(can you correct this 1 for me.)
tan (x+15)= 3 tan x

tan(x+15) = (tanx + tan15)/(1-tanx tan15)

(tanx + tan15)/(1-tanx tan15) = 3 tanx
tanx + tan 15 = 3 tanx - 3tan2x tan15
3 tan2x tan15 - 2tanx + tan15 = 0
tan15 = 0.27, denote tanx as t
0.81 t2 - 2t + 0.27 = 0
D = 0.1252
t1 = 1.67
t2 = 0.80


tan (x1) = 1.67
x1 = arctan (1.67) + ヰn = 59.087 + 180n = 59━ 5'+ 180n, n=0,1,2,..

tan(x2) = 0.80
x2 = arctan(0.80) + ヰn = 38.66 + 180n = 38━ 40' + 180n, n=0,1,2,..

Answer: 59━ 5', 239━ 5', 38━ 40', 218━ 40'

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