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April 16th, 2018, 10:19 AM   #1
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Question Trig double angles

Sin (x+60) = 2 Sinx

Solve for x

Last edited by Vee88; April 16th, 2018 at 10:30 AM.
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April 16th, 2018, 10:47 AM   #2
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sin(x)cos(60°) + cos(x)sin(60°) = 2sin(x)
tan(x)/2 + √3/2 = 2tan(x)
sqrt(3) = 3tan(x)
tan(x) = 1/√3
x = (30 + 180k)°, where k is an integer.
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April 16th, 2018, 10:56 AM   #3
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Question General Solution Trig

Determine the General Solution

4Cos^2 (-x) - Sin (2x -180)= Tan^2 675
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April 16th, 2018, 10:56 AM   #4
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Smile

Thank you for the above Skip
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April 16th, 2018, 11:46 AM   #5
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4cos²(-x) - sin(2x - 180°)= tan²(675$^\circ$)
4cos²(x) + sin(2x) = 1
4cos²(x) + 2sin(x)cos(x) = cos²(x) + sin²(x)
sin²(x) - 2sin(x)cos(x) + cos²(x) = 4cos²(x)
(sin(x) - cos(x))² = (2cos(x))²
sin(x) - cos(x) = ±2cos(x)
sin(x) = cos(x) ± 2cos(x) = -cos(x) or 3cos(x)
tan(x) = -1 or 3
x = (135 + 180k)$^\circ$ or arctan(3) + 180k$^\circ$
where (by use of a calculator) arctan(3) = 71.565051177...$^\circ$ and k is an integer.
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