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Exact trig. values

Free Printable Exact trig. values PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free exact trig. values worksheets (PDF), GCSE maths past paper questions and worked solutions for Exact trig. values (5V). 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, Corbett Maths, Maths Made Easy, M4ths.com, 1st Class Maths, Dr Austin, Naiker Maths, Metatutor, E Classroom and PMT, along with past paper question booklets.

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

Free Exact trig. values PDF Worksheets & Answers

Grade 5 • Topic 5V
Resource Questions Answers
Graded exam questions & solutions
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MME worksheet & model answers
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PMT (Edxl)
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PMT (AQA)
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PMT (IGCSE)
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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 Exact trig. values: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

For non-calculator exams, recall the exact values of sin θ, cos θ, and tan θ for 0°, 30°, 45°, 60°, and 90°. Derive them anytime from an isosceles right-angled triangle (legs 1, 1, hypotenuse √2) and an equilateral triangle of side 2 split in half (sides 1, √3, 2).

θ0°30°45°60°90°
sin θ012√22√321
cos θ1√32√22120
tan θ0√331√3—
45° 1 1 √2 60° 30° 1 2 √3

Example 1: Work out the exact value of sin 30° + cos 60° + tan 45°.

Solution:

Substitute: 12 + 12 + 1 = 2
Answer: 2

Example 2: Find the exact side x opposite 60° in a right-angled triangle with hypotenuse 12 cm.

Solution:

x = 12 × sin 60° = 12 × √32 = 6√3 cm
Answer: 6√3 cm
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Exact trig. values Questions & Answers

Past Paper Example 1 OCR Jun 2022 2F Q19 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Work out
(a) Circle the value of \sin 30°.
12   √(3)2   13   √(3)3   14
(b) Here is a right-angled triangle.
(a) Circle the value of \sin 30°.
12   √(3)2   13   √(3)3   14 [1 mark]
(b) Here is a right-angled triangle. [2 marks]
30°24 cmx cmNot toscale
Work out the value of x.
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
sin 30° = 1/2. B1
Answer (a): 1/2
Part (b) Solution:
sin 30° = x / 24 M1
⇒ x = 24 × sin 30° = 24 × 1/2 = 12. A1
Answer (b): x = 12
Past Paper Example 2 GCSE Nov 2018 1H Q8 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Write down the exact value of tan 45° (1) (b) Right-angled triangle with adjacent 4 cm, angle 60°, hypotenuse x cm. cos 60° = 0.5. Work out x. (2)
(a) Write down the exact value of \tan 45° [1 mark]
(b) Work out the value of x. [2 marks]
60°4 cmx cm
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
tan 45° = 1 B1
Answer (a): 1
Part (b) Solution:
cos 60° = 4 / x M1
⇒ 0.5 = 4 / x
⇒ x = 8 A1
Answer (b): 8
Past Paper Example 3 Specimen Set 1 1F Q26 / 1H Q7 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Write down the exact value of cos 30° (1) (b) Given that sin 30° = 0.5, work out the value of x in the right-angled triangle with hypotenuse 12 cm. (2)
(a) Write down the exact value of \cos 30° [1 mark]
(b) Given that \sin 30° = 0.5,
work out the value of x. [2 marks]
30°12 cmx cm
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
√(3)2
Answer (a): √(3)2
Part (b) Solution:
x / 12 = sin 30° = 0.5 M1
⇒ x = 12 × 0.5 = 6 A1
Answer (b): 6

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