SOLUTION: How do I solve the equation Find all solutions to Tan(theta-30 degrees)= -5 Book answers 131.3 and 311.3. I am not able to solve the equation and get the results of the correct a

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Question 1062077: How do I solve the equation Find all solutions to Tan(theta-30 degrees)= -5 Book answers 131.3 and 311.3. I am not able to solve the equation and get the results of the correct answers.
Found 2 solutions by math_helper, stanbon:
Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!

<<< ordinarily, this is acceptable b/c arctan(x) is by default expressed
as an angle between -90 and +90 degrees.
Now, "all solutions" adds a bit more work. We need to look to see where tan(x) is positive and where it is negative.
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Recall tan(x) = sin(x)/cos(x)
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Q1: sin(x) is +, cos(x) is + �> tan(x) is +
Q2: sin(x) is +, cos(x) is - �> tan(x) is -
Q3: sin(x) is -, cos(x) is - �> tan(x) is +
Q4: sin(x) is -, cos(x) is + �> tan(x) is -
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Therefore, all of the angles (0�360 degrees) that satisfy theta=-48.69 = arctan(x) are:
#1: -48.69 + 360 = 311.31 degrees (in Q4)
#2: -48.69 + 180 = 131.31 degrees (in Q2)
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Check:
#1: tan (311.31-30) = tan(281.31) = -5
#2: tan(131.31-30) = tan(101.31) = -5
�

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find all solutions to Tan(theta-30 degrees)= -5 Book answers 131.3 and 311.3. I am not able to solve the equation and get the results of the correct answers.
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arctan(tan(t-30)) = arctan(-5)
t-30 = -78.69 degrees
theta = = -48.69 deg = 360-48.69 = 311.31 degrees (Answer in QIV)
OR
theta = -48.69 degrees or theta = 180-48.69 = 131.31 (Answer in QII)
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Cheers,
Stan H.
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