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Answer on Trigonometry Question for Isha

Question #1755

Solve this trigonometric equation.give all positive values of the angle between 0deg and 360deg that will satisfy.<br>Give any approximate value to the nearest minute only.

<br>&nbsp;tan (x+15) = 3 tanx

Expert's answer

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) + πn = 59.087 + 180n = 59º 5'+ 180n, n=0,1,2,..

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

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


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