Question

cos θ = − root2 /2

Answer 1

how can you get rid of the cosine?

Answer 2

arc cos?

Answer 3

yep

Answer 4

do you know the unit circle?

Answer 5

yup

Answer 6

okay, so where is cos(θ) = -sqrt(2/2) ?

Answer 7

3pi/4

Answer 8

Yes.. correct.

Answer 9

what about 5pi/4 ?

Answer 10

now do u need general solution or within the range 0 to 2pi ?

Answer 11

these are the directionsSolve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)

Answer 12

means genearalized solution, can u generalize this ?

Answer 13

5pi/4 ,-5pi/4,3pi/4,-3pi/4

Answer 14

There is an infinite amount of solutions, you need to write it in a way to GENERALIZE the solution.

Answer 15

so let me generalize it.
cos function is periodic with 2pi.
so values repeat after every 2pi*k
here,
\(\theta =\pm(3\pi/4+2\pi k),\pm(5\pi/4+2\pi k)\)

Answer 16

ohh i see but why do u add the 2pik at the end ? because it is a periodic function?

Answer 17

yes, as i said cos function is periodic with 2pi.
so if a is solution, so is a+2pi, a-2pi,a+4pi,a-4pi, and so on

Answer 18

ohh i see i missed this whole lesson on this section and i dont know any of it