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Trigonometry (SOHCAHTOA)

Free Printable Trigonometry (SOHCAHTOA) PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free trigonometry (sohcahtoa) worksheets (PDF), GCSE maths past paper questions and worked solutions for Trigonometry (SOHCAHTOA) (5U). This is a Grade 5 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Dr Austin, Maths4Everyone, Corbett Maths, Maths Made Easy, Dr Frost, Naiker Maths, 1st Class Maths, Dr Frost (B. Blocks), Metatutor, IGCSE MT, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our trigonometry (sohcahtoa) revision notes and worked examples with diagrams, try real GCSE past paper trigonometry (sohcahtoa) questions with step-by-step solutions, or download a PDF of all trigonometry (sohcahtoa) worksheet links.

Free Trigonometry (SOHCAHTOA) PDF Worksheets & Answers

Grade 5 • Topic 5U
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
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Practice grid / worksheet & answers
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GCSE 9–1 practice booklet & solutions
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Practice Questions & answers
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Textbook Exercise & answers
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MME worksheet & model answers
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GCSE worksheet & solutions
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Exam question booklet & solutions
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Edexcel exam questions & solutions
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AQA exam questions & solutions
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Building Blocks skill sheet & answers
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Topic worksheet & worked solutions
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IGCSE (9–1) past paper booklet
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Online topic notes & examples
 Page
Interactive online lesson & practice
 Page
Self-marking online worksheet
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Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Trigonometry (SOHCAHTOA): Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

In a right-angled triangle, label the sides relative to the angle θ: H (Hypotenuse) is opposite the right angle, O (Opposite) is across from θ, and A (Adjacent) is next to θ.

Use SOHCAHTOA: sin θ = OH, cos θ = AH, and tan θ = OA. To find a missing angle, use the inverse buttons sin−1, cos−1, or tan−1.

Example 1: A right-angled triangle has hypotenuse 14 cm and angle 38°. Find the side x opposite the 38° angle (to 1 d.p.).

Solution:

O = x, H = 14 (SOH):
sin 38° = x14
x = 14 × sin 38° = 8.6 cm
38° 14 cm x

Example 2: In a right-angled triangle, the side opposite angle θ is 11 cm and the adjacent side is 9 cm. Find θ (to 1 d.p.).

Solution:

O = 11, A = 9 (TOA):
tan θ = 119
θ = tan−1(119) = 50.7°
θ 9 cm 11 cm
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Trigonometry (SOHCAHTOA) Questions & Answers

Past Paper Example 1 GCSE Jun 2025 2F Q26 / 2H Q7 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
ABC is a right-angled triangle.
ABC7 cm4 cmx°
Calculate the value of x.
Give your answer correct to 1 decimal place.
Worked Solution & Mark Scheme (2 marks)
tan(x) = opposite ÷ adjacent = 7 ÷ 4 = 1.75 M1
⇒ x = tan⁻¹(1.75) = 60.255... ≈ 60.3°. A1
Answer: x = 60.3
Past Paper Example 2 GCSE Nov 2022 2F Q22 / 2H Q5 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
53°x cm14.5 cm
Right-angled triangle with hypotenuse 14.5 cm, adjacent side x cm, and angle 53°. Work out x to 3 s.f.
Work out the value of x.
Give your answer correct to 3 significant figures.
Worked Solution & Mark Scheme (2 marks)
x = 14.5 × cos 53° = 8.7263... → 8.73 M1 A1
Answer: x = 8.73
Past Paper Example 3 AQA Jun 2018 1H Q25 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is a sketch of the graph of y = \cos x for values of x from 0° to 360°
xy1–100°90°180°270°360°
(a) \cos x = \cos 60°
Work out the value of x when 90° ≤ x ≤ 360° [1 mark]
(b) \cos x = -\cos 60°
Work out the value of x when 180° ≤ x ≤ 360° [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
By symmetry of the cosine graph: \cos(360° - x) = \cos x
So x = 360° - 60° = 300°. B1
Answer (a): Answer 300 degrees
Part (b) Solution:
\cos 60° = 0.5, so \cos x = -0.5
In the interval 180° ≤ x ≤ 360°, x = 180° + 60° = 240°. B1
Answer (b): Answer 240 degrees

← 5T Similar shapes (lengths)

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