Robinson Tuition
Grade 8 · Higher · free GCSE maths worksheet

Graphs of sin, cos and tan

Shape, period and solving equations.

12 original questions, 37 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

The curve C has equation y = cos x° for 0 ≤ x ≤ 360

  1. Write down the coordinates of the points where C crosses the x-axis.

  2. Write down the coordinates of the maximum points of C.

  3. Write down the coordinates of the point where C crosses the y-axis.

3 marks
Show answer
a) (90, 0) and (270, 0) b) (0, 1) and (360, 1) c) (0, 1)
2

  1. Write down the period of the graph of y = cos x°.

  2. Write down the period of the graph of y = tan x°.

  3. Write down the maximum value and the minimum value of y = 4 sin x°.

3 marks
Show answer
a) 360° b) 180° c) maximum 4, minimum -4
3

The curve C has equation y = cos x° for 0 ≤ x ≤ 360.

Write down the coordinates of the minimum point of C.

2 marks
Show answer
(180, -1)
4

You are given that sin 20° = 0.342, correct to 3 decimal places.
Use the graph of y = sin x° to write down the value of

  1. sin 160°

  2. sin 200°

  3. sin 340°

  4. cos 70°

4 marks
Show answer
a) 0.342 b) -0.342 c) -0.342 d) 0.342
5

You are given that tan 35° = 0.700, correct to 3 decimal places.

  1. Find all the solutions of tan x° = 0.700 for 0 ≤ x ≤ 360

  2. Find all the solutions of tan x° = −0.700 for 0 ≤ x ≤ 360

3 marks
Show answer
a) 35 and 215 b) 145 and 325
6

Sketch the graph of y = tan x° for 0 ≤ x ≤ 360.

Show clearly where the graph crosses the x-axis and mark the values of x where the graph has asymptotes.

090180270360−4−3−2−11234x (degrees)y
2 marks
Show answer
Correct tan shape: branches through (0,0), (180,0), (360,0) with vertical asymptotes at x = 90 and x = 270
7

Solve 5 sin x° = 2 for 0 ≤ x ≤ 360
Give your answers correct to 1 decimal place.

3 marks
Show answer
x = 23.6 and x = 156.4
8

You are given that sin 40° = 0.643 correct to 3 decimal places.

Using the symmetry of the graph of y = sin x°, write down the two solutions of

sin x° = 0.643 for 0 ≤ x ≤ 360

Give the angle solutions to the nearest whole degree, using the supplied approximation.

090180270360−11x (degrees)y
2 marks
Show answer
x = 40 and x = 140
9

Solve cos x° = −0.3 for 0 ≤ x ≤ 360
Give your answers correct to 1 decimal place.

3 marks
Show answer
x = 107.5 and x = 252.5
10

You are given that cos 60° = 0.5

  1. Find all the solutions of cos x° = 0.5 for 0 ≤ x ≤ 360

  2. Find all the solutions of cos x° = −0.5 for 0 ≤ x ≤ 360

3 marks
Show answer
a) x = 60 and x = 300 b) x = 120 and x = 240
11

  1. Sketch the graph of y = sin x° for 0 ≤ x ≤ 360, marking the values where the graph meets the x-axis.

  2. You are given that sin 35° = 0.574 correct to 3 decimal places.

    Find all the solutions of sin x° = −0.574 for 0 ≤ x ≤ 360

Give the angle solutions to the nearest whole degree, using the supplied approximation.

090180270360−11x (degrees)y
4 marks
Show answer
a) Sine wave through (0,0), (180,0), (360,0) with maximum (90, 1) and minimum (270, -1) b) x = 215 and x = 325
12

The curve C has equation y = 2 sin x° + 1 for 0 ≤ x ≤ 360

  1. Write down the coordinates of the maximum point of C.

  2. Write down the coordinates of the minimum point of C.

  3. Write down the coordinates of the point where C crosses the y-axis.

  4. Solve 2 sin x° + 1 = 0 for 0 ≤ x ≤ 360

5 marks
Show answer
a) (90, 3) b) (270, -1) c) (0, 1) d) x = 210 and x = 330

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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