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Want to know about solving angles..

in C3 , sometimes we may get into tan2A = something or Sin3A something.

ppl said i have to increase the range and half the angle ...

but i have no idea why and how i can remember those rules easily?

thanks again
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Avatar for Jooeee
Jooeee
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So say if you need to solve for θ \theta in the range 0≤θ≤π 0\leq\theta\leq\pi and you have sin⁡2θ=12 \sin{2\theta}=\frac{1}{2} then when you do inverse sin you're going to have your principal solution π6 \frac{\pi}{6} (the one the calculator gives and by symmetry of the graph a solution at π−π6=5π6 \pi-\frac{\pi}{6}=\frac{5\pi}{6}

But note that this is 2θ 2\theta and so we must half our answers to get θ \theta . So can you see now that we should include π6+2π \frac{\pi}{6}+2\pi and 5π6+2π \frac{5\pi}{6}+2\pi as when we halve these they will still be included in our range.

I don't change the range or anything all i do is solve it like i did before and add on 2pi, pi depending on if it's sin/cos or tan and then halve/divide by 3 or whatever and see if that's still included in the range.

Another way to think about why is if you have the graph y=sin⁡x y=\sin{x} transformed on to the graph y=sin⁡ax y=\sin{ax} then it has undergone a transformation of a stretch parallel to the x-axis of 1a \frac{1}{a} and so if we were to plot the line y=0.5 say then it will intersect the graph a more times in the range 0 to 2pi than it did before the transformation.
i change the range. after getting the answer i eualise them with 2\theta or 3\theta and solve them..it is much easier for me...

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