Question

Find the sum of trigonometric equation solution in the range of [0,2pi]:

Answer 1

\[\cos2x+\sin^2x=\frac{ 3 }{ 4 }\]

Answer 2

@AravindG @ganeshie8 @mathstudent55 @eliassaab @thomaster @SolomonZelman @hoblos

Answer 3

\[cosx= \frac{ \sqrt{3} }{ 2 }\]

Answer 4

but i don't have the full answer

Answer 5

\[\cos(2x) = \cos^2 (x) - \sin^2(x)\]

Answer 6

i solved the exercise
but i don't know how to finalize it

Answer 7

OK. Do you know the angles for which \(\cos(x) = \dfrac{\sqrt{3}}{2}\)?

Answer 8

yes pi/6
i guess..

Answer 9

Good job.

Answer 10

actually it's not

Answer 11

Read again the exercise!

Answer 12

hmm, isn't that what the question asks for?

Answer 13

Oh, it looks for the sum of all angles. I think.

Answer 14

yes

Answer 15

OK, then look at your unit circle.

Answer 16

\[\cos(2\pi - x) = \cos(x)\]So \(2\pi - \pi/6\) also is an angle.

Answer 17

so do you mean cos it's a periodical function of 2pi period?

Answer 18

OK, let's look at the unit circle. That'd explain everything.

cos is the x-coordinate on the unit circle, right?

Answer 19

right