C2 Trig Help!

for c2 you only learn 2 things:

cos^2 x + sin^2 x =1

tanx=(sinx)/(cosx)

sin is postive for angles between 0 and 180 and negative 180< to 360, cos is positive for angles 0 to 90 and 270 to 360 negative 90-270

use these in a) and b) in a way you think helps you the most.......

a) Find all possible values of sin C for which cos C = 1/2.
b) Find the values of D for which -180 degrees <D< 180 degrees and tan D = 5 sin D.

Right so for part a), I did cos-1 (1/2) = 60, and then sin 60 = root 3 / 2. I am told that this is one of the answers, and the other is meant to be - root 3 / 2, how do I get this?

I don't know how to approach part b), so any help on both would be really appreciated thanks!

awwwwwwwww, its been about 7 months since i didnt do any maths, i miss it lol

the first part is this:
cos^2 C + sin^2 C = 1
cos ^2 C = 1/4
sin^2 C = 1 - 1/4 = 3/4
sin C = root(3) / 2 = pi / 3 (Im not sure, double check on calculator)
and then depending on the range, there are certain other answers, i think you can do it from here.

second part:
tan D = 5sin D
sin D / cos D = 5 sin D
sinD / sind D = 5 cos D
cos D = 1/5
and calculate this on your calculator
i hope this helps)

you get $- \frac{\sqrt3}{2}$ by looking at your graph of $y=cosx$ and figuring out that there is another value C for which $cosC=\frac{1}{2}$
I'm assuming somewhere in the question it says $-180\le C \le 180$

for b, I'd try to find a value D for which both sind and tand = 0. because then 5sind and tand will = 0.

I am asking how to do it without a graph And nope, in the question it just says "all possible values". And oh right you are right there

oh no, actually what am I thinking, C doesn't need confining
I apologise.

and really, you should just be able to sketch out a graph of y=cosx. though you needn't actually use it for that question, you should just know that $cos60=0.5$ and that $cos(-60)= 0.5$

I see Thanks for the help For the second part, once you get cos D = 1/5, you calculate D to be 78.46 degrees, but the answers at the back say that you should get 78.46 (which I have got), -78.46 and 0. Any idea how to get the other 2 answers?

erm, i know how to get -78.46 , cos X = cos (-X) for any value of X, i.e. cos 78.46 = cos (-78.46).
but for 0, i dont know ( for 0, cos X = 1, which we didnt get, we got cos X = 1/5.. sorry

Oh right so is cos X = cos (-X) a general rule which only applies for cos?

for c2 you only learn 2 things:

cos^2 x + sin^2 x =1

tanx=(sinx)/(cosx)

sin is postive for angles between 0 and 180 and negative 180< to 360, cos is positive for angles 0 to 90 and 270 to 360 negative 90-270

use these in a) and b) in a way you think helps you the most.......