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# Higher Maths Trigonometry help watch

1. Just now I am doing trigonometric equations like

cos2x - sinx = 0

the formula I am supposed to use is 1 - 2sin^2x

can anyone do that explaining it fully, especially the bit with the cast diagram, how do I know how many values and what ones to find out?
2. Take:

And put it into the equation:

to get:

Rearrange to get a nice(ish) quadratic:

And I'm sure you know how to get sinx:

And solve for x.
Hope it helped.
3. cos(a+b) = cosacosb - sinasinb

Writing cos2x as cos(x+x) = cos^2 x - sin^2 x [where cos^2 x = (cosx)^2 etc]

Using cos^2 x + sin^2 x = 1 you can replace cos^2 x and sin^2 x in the above expression.

i.e. 1 - 2sin^2 x

So your equation becomes (1 - 2sin^2 x) - sinx = 0
4. Thanks for your help I understand it much better now, but one last thing. How do I use the CAST diagram (cos all sin tan) to work out which values of x to find?

I have 30 and 270 but the answer also has 150
5. I find the best way is to sketch the graph on sinx between 0 and 2pi

Remember your calculator is only giving you one value for arcsin ....whatever you put. If you draw a line through the graph where x = 1/2 (one of the answers for what sinx equals) you can see it intersects at pi/6 and pi-pi/6, or 30 and 180 - 30

Doing the same for when x=-1, you see if only intersects once in this region, at 270.
6. Oh right, I think I get you now, thanks for the help

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