Question

How do you solve `10sin(x-2)=-7`?

Answer 1

`70^@22 and 339^@08` for (0, 360)

Explanation:

First convert 2 radian to degrees
3.14 --> 180^@
1 radian --> 180/(3.14)
2 radian --> `(2(180))/3.14 = 360/3.14 = 114^@65`
The equation becomes:
10sin(x - 114.65) = - 7
sin (x - 114.65) = -7/10 = - 0.7
Calculator and unit circle -->
Arc `(x - 114.65) = - 44^@43`
arc (- 44.43) is co-terminal to arc `(360 - 44.43 = 315^@57)`
and arc `x - 114.65 = 180 + 44.43 = 224^@43`
a. x - 114.65 = 224.43 --> `x = 339^@08`
b. x - 114.65 = 315.57 --> `x = 430^@32`, or `70^@22`
Answer for (0, 360):
`70^@22; 339^@08`