Trigonometry: worked exam questions
15 solved trigonometry questions, each worked line by line the way the 0606 mark scheme rewards. Learn the method in the Trigonometry topic notes, then see it applied here.
Amplitude, Period and Counting Solutions
Read the amplitude, period, maximum and minimum of y = a + b sin(cx), then count how many solutions an equation has in a given range, a 0606 graph question.
Exact Trig Values from a Given Ratio
Given sinθ and that θ is obtuse, find the exact values of cosθ and tanθ, a 0606 Paper 1 question that tests the quadrant sign rule and the Pythagorean identity.
Exact Values of Special Angles
Evaluate an expression exactly using the special-angle values, a 0606 Paper 1 non-calculator question testing recall of sin, cos and tan at 30, 45 and 60 degrees.
Exact Values Using Double-Angle Formulae
Given sin θ, find sin 2θ and cos 2θ exactly using the double-angle formulae and a right triangle, a standard 0606 trigonometry question.
Proving a Reciprocal Trig Identity
Prove sec²x + cosec²x = sec²x·cosec²x by writing everything over a common denominator, a 0606 identity proof using the reciprocal functions.
Proving a tan² Identity
Prove that (1 − cos²x)/cos²x = tan²x using the Pythagorean identity, a short 0606 identity proof built on two familiar relationships.
Proving a Trigonometric Identity
A 0606 identity proof worked from one side only, the disciplined layout examiners reward, with the Pythagorean identity doing the heavy lifting.
Proving an Identity with tan and cot
Prove that tan x + cot x = 1/(sin x cos x) by converting to sines and cosines, a 0606 identity proof that shows the go-to first move.
Solving a Cosine Equation in Radians
Solve cos x = −0.5 over 0 to 2π, a 0606 trig question testing radian solutions and the quadrants where cosine is negative.
Solving a Quadratic Trigonometric Equation
Solve a 0606 trig equation that hides a quadratic: swap sin² for 1 − cos², factorise, reject the impossible root, then find every angle in range.
Solving a Tangent Equation in a Range
Solve tan(2x) = 1 over a given interval, a 0606 trig question where tan's 180-degree period and the doubled argument both matter.
Solving a Trig Equation Using an Identity
Turn a mixed tan-and-cos equation into a quadratic in sin using Pythagorean identities, then solve over 0 to 360 degrees, a classic 0606 question.
Solving a Trig Equation with a Multiple Angle
Solve sin(2x) = 0.5 in a given range, a 0606 trig question where the doubled argument means widening the search interval to catch every solution.
The R-Formula: Solving and Finding a Maximum
Express a sinθ + b cosθ as R sin(θ + α), then use that form to solve an equation and read off the maximum. Extension practice, not in the 0606 syllabus.
Transformations of a Trig Graph
Sketch y = 2 sin x + 1, reading the amplitude, period and range from the transformation, a standard 0606 trig-graph question.
Worked examples show the routine. A tutor builds it into your child.
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