Question

So I have a part of this solution that I don't quite understand, if someone could please explain it to me? ^^

find all angles between 0 and 360 degrees that satisfy:
cos2x=0.5

this chapter is trig identities & equations
the basic angle chappie

apparently the answer lists 2x as the following
π/3
5π/3
π/3+2π
5π/3+2π

and multiply that by 2 to get
π/6
5π/6
π/6+2π
5π/6+2π

but how did they get those?
isn't cos2x=0.5
2x=cos^-1(0.5)?
i can't see the link

Answer 1

okay actually i do see the link but only between cos^-1(0.5) and π/3
where did the rest come from??

Answer 2

oh yeah and i just realised i typed conflicting units of π and ˚
they're all in π so
π<x<2π
sorry about that

Answer 3

@PaxPolaris if you know something about trig? ^^

Answer 4

what don't you get? .... are you asking why there is more than one answer?

Answer 5

yeap, i'm asking why there are 4 answers when there can only be two possible quadrants
and why they exceed 2π but are accepted

Answer 6

you have to find all x that are between 0 and 2π

so 2x is between 0 and 4π

Answer 7

so the limits automatically change from 2π to 4π?

Answer 8

if the limit for x is 2pi.

then you have to multiply by 2 to get the limit of 2x

Answer 9

ohh i see it now

so the 2x is a fixed value? like, i don't have to divide to get just x?

Answer 10

the range of 2x is til 4pi.


so you get 4 values for 2x:
π/3
5π/3
π/3+2π
5π/3+2π

then you divide by 2 to get the values of x:
π/6
5π/6
π/6+π ***
5π/6+π ***

(*** you had copied the last two wrong). x is still between 0 and 2pi.

Answer 11

no the answer does state it as 5π/3+2π
in fact, they further combined it to get 11π/3...

Answer 12

and then they put it as x=11π/6
does that mean that in the end, i'll have to divide all my answers by two and then see if they fit into the limits before rejecting or not?

Answer 13

lets look at a different question: tan (3z) = 1 .... and i tell you z has to be between 0 and pi

you have to be careful finding the range of 3z :\[0<3z<3\pi\] you get 3 answers for 3z....
when dividing to get z, as long as you divide correctly ... your answer is automatically in the correct range.

Answer 14

ah okay thank you :3