Question

Question #72dcf

Answer 1

`x = 74^@14 + k360^@`
`x = - 51^@52 + k360^@`

Explanation:

cos x + (0.2)sin x = 0.466
Call t the arc that tan t = 0.20 --> `t = 11^@31`--> cos t = 0.98
`cos x + ((sin t)/(cos t))sin x = 0.466`
`cos x.cos t + sin t.cos x = (0.466)cos t = (0.466)(0.98) = 0.457`
Use trig identity:
cos (x - t) = cos x.cos t - sin t.sin x
In this case:
`cos (x - 11.31) = 0.457 = cos 62^@83`
`x - 11.31 = +- 62.83`

a. `x - 11.31 = 62.83` --> `x = 63.83 + 11/31 = 74^@14`
b. x - 11.31 = - 62.83
`x = 11.31 - 62.83 = - 51^@52`
General answers:
`x = 74^@14 + k360^@`
`x = -51^@52 + k360^@`