General Solution of Circular Function Equations

[mandy]

Find the general solution to each of the following equations:
a.
b.
c.

I only got given the questions, with no explanation, so I have no idea what it's asking me to do. Could someone help me with part a? Then maybe I'll be able to do the other parts on my own. Thank you.

[TrueTears]

cosx = 1/2

x = pi/3+2pi(k), 5pi/3+2pi(k) where k is an element of Z

[the.watchman]

(a) For ,



so the general solution is , where n is an integer

The n signifies that solutions occur every 2pi

TT, you beat me!

[TrueTears]

ok.

[mandy]

Oh, thank you the.watchman and TrueTears, now I'll try part b :]

[mandy]

For part b,

b.

I got , but the answer is . How do I know whether to have a plus minus, or only a plus?

[TrueTears]

you dont need + or - since n takes that into account, remember n \in Z

[the.watchman]

Ah, I think I know your mistake, sin is not symmetrical about the y-axis, so you can't really use the plus/minus approach
Instead, find the solutions in [0,2pi], then add 2npi to them and divide by 3

Good luck!

[the.watchman]

you dont need + or - since n takes that into account, remember n \in Z

Doesn't the plus/minus suggest solutions ABOUT rather than ?

[mandy]

Thanks again guys :]

[the.watchman]

Thanks again guys :]

No problems! xD

[TrueTears]

np

[mandy]

Oh no, one more problem, lol.
Part c. How come the answer is and not  , which is what I got?

[TrueTears]

answer can be pi n + pi/3

[the.watchman]

First, the period for a tan graph is , not

So shouldn't the answer be ?