Precalculus Trigonometric Identities Quiz: 10 Questions with Explanations

A \(\sin2x\)B 1C 0D \(2\sin x\cos x\)

This is the Pythagorean identity.

A \(\frac{\cos x}{\sin x}\)B \(\sin x\cos x\)C \(\frac{1}{\sin x}\)D \(\frac{\sin x}{\cos x}\)

Tangent is sine divided by cosine; the reciprocal is cotangent.

A \(2\sin x\)B \(2\sin x\cos x\)C \(\sin^{2}x\)D \(\cos^{2}x-\sin^{2}x\)

The double-angle formula for sine is 2 sin x cos x.

A \(1-2\sin^{2}x\)B \(2\sin x\cos x\)C \(1+2\sin^{2}x\)D \(2\cos x\)

cos 2x = cos^2 x – sin^2 x = 1 – 2 sin^2 x.

A \(\sin2x=2\sin x\)B \(\sin2x=\sin x+\cos x\)C \(\sin2x=2\sin x\cos x\)D \(\sin2x=\cos2x\)

The curves y = sin 2x and y = 2 sin x cos x are identical.

A \(\sin A+\sin B\)B \(\sin A\cos B-\cos A\sin B\)C \(\sin A\cos B+\cos A\sin B\)D \(\cos A\cos B-\sin A\sin B\)

The sine sum formula has a plus sign between the two products.

A The constant 1B The constant 0C \(\sin2x\)D \(\cos2x\)

sin^2 x + cos^2 x = 1 for all x, the dashed horizontal line.

A \(\frac{\sqrt6-\sqrt2}{4}\)B \(\frac{\sqrt6+\sqrt2}{4}\)C \(\frac{\sqrt3}{2}\)D \(\frac{\sqrt2-1}{2}\)

sin(45 – 30) = (sqrt2/2)(sqrt3/2) – (sqrt2/2)(1/2). A plus sign would give the cos 15 value.

A \(\frac14\)B \(\frac12\)C \(\frac{\sqrt3}{2}\)D \(-\frac12\)

cos 2x = 1 – 2(1/4) = 1/2.

A Divide both sides by \(\sin x\)B Replace \(2x\) by \(x\)C Take the arcsine of both sidesD Write \(2\sin x\cos x-\sin x=0\) and factor

Dividing by sin x would lose the solutions where sin x = 0. Move everything to one side and factor.