Question 1117559: Could someone give me some tips about how to solve this question ? I don't know how to do this question with decimals. Thanks you!
Give the smallest two solutions of cos(6θ) = 0.2771 on [ 0,2π ).
Separate the two solutions with a comma.
Be sure to round only once at the end.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Could someone give me some tips about how to solve this question ? I don't know how to do this question with decimals. Thanks you!
Give the smallest two solutions of cos(6θ) = 0.2771 on [ 0,2π ).
Separate the two solutions with a comma.
Be sure to round only once at the end.
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The last sentence needs to specify how many decimal places (which I'd expect to be 4 or less, because the value 0.2771 has 4 signficant digits). I will carry 7 decimal digits for all the calculations and you can round to the required number of digits.
Step-by-step:
Now, there are two solutions, the one above (in Q1), and  (in Q4).
This is because x is positive in Q1 and Q4, thus  has positive x in those two quadrants. I am referring to {{ 6* theta }}} here, finding  itself requires dividing by 6.
Solving the two cases for  you should get  rad for the Q1 angle and  rad for the Q4 angle.
A graph might help visualize this, where A and B are the approximate locations of the two solutions:
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EDIT 5/30/18:
In my post, I was referring to the quadrants of  not itself. For clarity, let  then it was  in Q1 and Q4. I did mention this fact and I apologize if it was not clear.
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
I'd like to make one notice (correction) to the solution by the tutor @Math_helper.
He correctly found one solution theta_1 = 0.215 radians in Q1.
He also correctly found the other solution theta_2 =  = 0.831 radians, but mistakenly referred to it as to the angle of Q4.
In fact, the angle theta_2 lies in Q1, too.
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