Question

Solve "cos (2x) = sin (x) - 2" for [0,2Pi)

Answer 1

cos (2x) = sin (x) - 2
Convert to 1-2sin^2(x)
1-2sin^2(x)= sin (x) - 2
2sin^2(x)+sin(x)-3=0
(sin(x)-1)(2sin(x)+3)=0
sin(x)=1 sin(x)=-3/2
Then use this to solve for x

Answer 2

How would you use that chart? I always have trouble negotiating positive/negative values in trig, and it's a very important concept in advanced trig.

Answer 3

According to the graph, the solution is pi/2

Answer 4

But I would like to know how this works algebraically

Answer 5

sin(x)=1 sin(x)=-3/2
Doing sin(x)=1,
\[x=\sin^{-1}(1)\]
x=90
Then you need to get another value from the chart
This sin(x)=1 is positive, so you look at the positive side
so, 180-90 and get another value
x=90 but its the same.
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We move on to
sin(x)=-3/2
\[x=\sin^{-1}(-3/2)\]
No solution .
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x=90 only