Solving Within an Interval & Finding the Period

*1) Find the solutions of http://i.imgur.com/BtdJaZQ.pngin the interval http://i.imgur.com/FH51U7A.png*

I can determine that there are 4 solutions that need to be found, but I can only find 2 of them (http://i.imgur.com/yd5UOCc.png). How do I find the others?

*2) Find the period of the graph http://i.imgur.com/CBshEEa.png*

I know how to find the period of functions containing either sin or cos, but not both. Can someone give me a crash course on how to do this?

Thanks in advance.

(Apologies for the choppy equation structure.)

Re: Solving Within an Interval & Finding the Period

Draw a unit trigonometric circle, find the value on y-axis, and . Draw a line parallel to x-axis that runs trough on the y-axis. The line intersects the unit circle in two distinct points - numbers that are at those two points on the trigonometric circle are the solutions to the given equation.

All of the solutions can be found solving and , .

Re: Solving Within an Interval & Finding the Period

1) Remember that When you find a solution to the equation you can add 2*pi to it again and again to get more solutions but you have an upper limit so the number of solutions will be limited.

2) The period P will satisfy the equation f(x)=f(x+P)

Re: Solving Within an Interval & Finding the Period

I realise that my suggestion for part 2) is very difficult if not impossible to solve.

You cannot guarantee this will be the smallest value of p to satisfy the equation but the function will repeat if there is a value y so that and

Remember that

same for cos

y will have to be an integer

Re: Solving Within an Interval & Finding the Period

Quote:

Originally Posted by

**MathoMan**
All of the solutions can be found solving

and

,

.

I'm not quite sure I fully understand. What's the value of *k*?