SOLUTION: If possible, find a solution to tan(2θ+7)=−11 . If no solution exists, enter NONE.

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Question 958137: If possible, find a solution to tan(2θ+7)=−11 . If no solution exists, enter NONE.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
tan%282%2Atheta%2B7%29+=+-11
If all you need is one solution (there are infinitely many), then all you need to do is...
Find the inverse tan of each side:
tan-1(tan%282%2Atheta%2B7%29) = tan-1(-11)
The left side simplies and the calculator will give us an number for the right side:
2%2Atheta%2B7 = -84.8 (degrees, rounded-off)
Now subtract 7 from each side:
2%2Atheta = -91.8 (degrees, rounded-off)
And divide by two:
theta = -45.9 (degrees, rounded-off)

All the other solutions will be multiples of 180 (since the period of tan is 180) away from -45.9.

In response to the question in your "Thank you" note:
To turn -45.9 into radians:
-45.9+%2A+%28pi%2F180%29+=+-0.255%2Api
If this is not the answer provided, then try adding various multiples of pi (since the period of tan, in radians, is pi) until you get the answer. For example:
-0.255%2Api%2Bpi+=+0.745%2Api

-0.255%2Api%2B2%2Api+=+1.745%2Api

If the "official" answer does not have pi in it, then replace pi with 3.141529 (or some rounded-off version of this decimal).