Question

Please help, precalc test tomorrow! Question is find all solutions on interval 0 less than or equal to theta less than or equal to 2 pi for cos(2theta)+1=0 I'm confused on how to get 2theta.....

Answer 1

do you remember the cosine of (2 *angle) =

cos(2x) = cos2(x) – sin2(x) = 1 – 2sin2(x) = 2cos2(x) – 1

those "double angle" identities they probably derived for you in trig awhile back

Answer 2

I've never taken trig

Answer 3

ok, well they are listed in trig identity tables... sorry the past there was bad

\[\cos(2x) = \cos^2(x)-\sin^2(x) = 1 - 2*\sin^2(x) = 2*\cos^2(x) - 1\]

Answer 4

algebra 2 class you may have seen it, alg2/trig

Answer 5

you can use one of those, or just see that

cos(2*angle) = -1

the cosine value is -1 for a certain angle in the circle, the -x direction , 180 deg, pi

Answer 6

cos(u) = -1

u = pi

so 2*angle has to be pi

angle is then pi/2

Answer 7

Ok.... so how did you get from 2cos^2theta-1 = cos(2theta)=-1?