Title: InkMaths / Trigonometry: identities and equations
On every note of this deck, unless a note says otherwise:
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Front: SPOT THE ERROR
Say what is wrong with this claim:
sin 2θ is 2 sin θ.
Back: sin 2θ = 2 sin θ cos θ. Trig functions do not come out of a bracket like a factor. Try θ = 30°. sin 60° is about 0.87, while 2 sin 30° is exactly 1. The same goes for cos 2θ and tan 2θ, which have their own double angle formulae.

Front: RECALL
State how to find R and α in the harmonic form.
Back: Expand R sin(θ + α) and match coefficients. R is the square root of the sum of their squares, and tan α is the cos coefficient over the sin one. Take R positive and read α's quadrant off the signs of the two coefficients: acute only when both are positive, and −3 sin θ + 4 cos θ needs 126.9°. Maximum R and minimum −R follow.

Front: STANDARD RESULT · LEARN IT
cos 2θ, all three forms:
cos 2θ = ?\(\cos 2θ = ?\)cos 2θ = ?
Back: cos ^2θ - sin ^2θ = 2cos ^2θ - 1 = 1 - 2sin ^2θ\(\cos^{2}θ - \sin^{2}θ = 2\cos^{2}θ - 1 = 1 - 2\sin^{2}θ\)cos^2θ - sin^2θ = 2cos^2θ - 1 = 1 - 2sin^2θ

Front: RECALL
State what to do with the interval when the equation contains 2x.
Back: Widen it first. If x runs over 0 to 360 degrees then 2x runs over 0 to 720, so solve for 2x across the wider range and halve every answer at the end. Solve in the original range and you find half the solutions and lose half the marks.

Front: STANDARD RESULT · LEARN IT
Small angle approximations, θ in radians only:
sin θ ≈ ?, cos θ ≈ ?, tan θ ≈ ?\(\sin θ \approx ?, \cos θ \approx ?, \tan θ \approx ?\)sin θ ≈ ?, cos θ ≈ ?, tan θ ≈ ?
Back: θ, 1 - θ^22, θ\(θ, 1 - \frac{θ^{2}}{2}, θ\)θ, 1 - (θ^2/2), θ

Front: STANDARD RESULT · LEARN IT
The other two Pythagorean identities:
sec^2 θ = ?, cosec^2 θ = ?\(\text{sec}^{2} θ = ?, \text{cosec}^{2} θ = ?\)sec^2 θ = ?, cosec^2 θ = ?
Back: 1 + tan^2 θ, 1 + cot^2 θ\(1 + \text{tan}^{2} θ, 1 + \text{cot}^{2} θ\)1 + tan^2 θ, 1 + cot^2 θ

Front: SPOT THE ERROR
Say what is wrong with this claim:
The sine rule gives sin B = 0.6, so B = 36.9° and the triangle is settled.
Back: 180° − 36.9° = 143.1° has the same sine, so there are two triangles unless the data rules one out. Check whether the obtuse option still leaves the angles summing under 180°, and whether the side opposite is long enough. The cosine rule never has this problem, because cosine is negative for obtuse angles and picks one answer.