3 · IB Maths AA
Compound angle and double angle identities
A right-angled triangle of hypotenuse 1 is rotated through angle A inside a rectangle, so the heights and widths add up to sin(A + B) and cos(A + B). Drag the points or use the sliders, then switch to double angle mode.
Try this
- Set A = B = 45°. Compare sin(A + B) with sin A + sin B to see why the sine of a sum is not the sum of the sines.
- Press Play so the triangle rotates through A. Watch the two gold segments always stack to the height of P, and explain why the angle at Q is also A.
- In double angle mode, find the A that makes cos 2A = 0 and check all three forms of cos 2A agree; then find where sin 2A is largest.
Common error: writing sin(A + B) = sin A + sin B or cos 2A = 2 cos A; always expand with the identity, then pick the cos 2A form that matches the function you already have (only cos A, or only sin A).