Posted by **Jossie** on Thursday, March 21, 2013 at 4:19am.

determine the general solution...2.sin(2x+30)=tan 135

- mathematics -
**Reiny**, Thursday, March 21, 2013 at 9:40am
The 135 suggests that you are working in degrees, so

2 sin(2x+30) = tan 135°

2sin(2x+30) = -1

sin(2x + 30) = -1/2

sine is negative in III and IV

so 2x+30 = 210 or 2x+30 = 330

2x = 180 or 2x = 300

x = 90 or x = 150

The period of sin(2x+30) is 360°/2 or 180°

so general solutions are:

90° + 180k° or 150° + 180k°

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