Question

Question #89a8f

Answer 1

`78^@69; 258^@69`

Explanation:

Use 4 trig identities:
`sin t - cos t = sqrt2sin (t - pi/4)`
`sin t + cos t = sqrt2sin (t + pi/4)`
sin (a - b) = sin a.cos b - sin b.cos a
sin (a + b) = sin a.cos b + sin b.cos a
In this case:
`3sqrt2sin (t - pi/4) = 2sqrt2sin (t + pi/4)`
`3sin (t - pi/4) = 2sin (t + pi/4)`
`3((sqrt2sin t)/2 - (sqrt2cos t)/2) = 2((sqrt2sin t)/2 + (sqrt2cos t)/2)`
`(sqrt2/2)sin t - (5sqrt2)/2cos t = 0`

sin t - 5cos t = 0
Call `tan x = sin x/(cos x) = 5` --> `x = 78^@69`
sin t cos x - sin x cos t = 0
sin (t - x) = sin (t - 78.69) = 0

Unit circle gives 2 solutions
`t - 78.69 = 0` --> `t = 78^@69`
`t - 78.69 = 180` --> `t = 258^@69`