Find the minimum value of the following expression and the value of x between 0 and 360 when the minimum occurs .
3 cos 2x + sin 2x --- this is the expression
3 cos 2x + sin 2x = r cos(2x-a)
tan a=1/3 , a =18.43
When minimum occurs , \sqrt{10}cos(2x-18.43)=-\sqrt{10}
cos(2x-18.43)=-1
2x-18.43=180 or 2x-18.43=270
Then i get my 2 values of x from there .
But i am wrong . Where is my mistake >?
I have not looked at the first part of your work, but this caught my eye:
That should be 540°, not 270°. The minimum values of the cosine function occur at odd multiples of 180°.cos(2x-18.43)=-1
2x-18.43=180 or 2x-18.43=270
Now, although we have the restriction , you have a 2x, which means that . That's why the 2nd number above should be 540°.
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