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Additional Maths - Need help with trig. equation problem

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1. How do you re-arrange equations such as 'Cosθ=Cos65°' to find solutions for theta? I understand what to do once it's simplified to ' θ=...', but I don't know how to get to that point when Cos is on both sides of the equation
2. sketch the cos graph. draw a vertical line at the 65º position on the x axis. then draw a horizontal line where this meets the curve. look along the horizontal line for further intersections with the curve.
3. (Original post by Tasha_140)
How do you re-arrange equations such as 'Cosθ=Cos65°' to find solutions for theta? I understand what to do once it's simplified to ' θ=...', but I don't know how to get to that point when Cos is on both sides of the equation

it is answer -65 because in cosine rule, cos(-x)=cos(x)
4. (Original post by Tasha_140)
How do you re-arrange equations such as 'Cosθ=Cos65°' to find solutions for theta? I understand what to do once it's simplified to ' θ=...', but I don't know how to get to that point when Cos is on both sides of the equation
Just find values of θ for which cosθ = cos(65°). Simples.

There are in fact infinitely many of these, however you know that a cos graph repeats every 360°, and is symmetric about the y-axis. Thus you can represent all solutions in the form 360n ± 65°, where n is an integer.
5. Got it, wasn't thinking properly, for some reason I thought I had to re-arrange...
Yea, prefer to use the CAST diagrams to the graphs themselves as I find it a lot easier haha, but thanks!

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