A student is asked to solve the equation sin2x=1\sin^2 x = 1sin2x=1 for 0°⩽x⩽360°0° \leqslant x \leqslant 360°0°⩽x⩽360°.
The student writes:
Step 1: sinx=1\sin x = 1sinx=1
Step 2: x=90°x = 90°x=90°
Explain the error the student has made in Step 1.
State the correct solutions of sin2x=1\sin^2 x = 1sin2x=1 for 0°⩽x⩽360°0° \leqslant x \leqslant 360°0°⩽x⩽360°.
A second student solves the equation sinxcosx=sinx\sin x\cos x = \sin xsinxcosx=sinx for 0°⩽x<360° 0° \leqslant x < 360°\,0°⩽x<360° by dividing both sides by sinx\sin xsinx, obtaining cosx=1\cos x = 1cosx=1 and hence x=0°x = 0°x=0°. Explain what is wrong with this method, and give the complete solution set.
317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.