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Common Trigonometric Ratios

Finding the exact values of sine, cosine and tangent of special angles.

Menu Level 1 Level 2 Level 3 Level 4 Level 5 Exam-Style Help More Trig

For the first six questions evaluate the expressions. For the final six questions find \(x\) where \( 0 \le x \le 90 \).

\( \sin60° \times \tan60° + \cos60° \)

Correct Wrong

\( 2\cos30° \times 3\tan30° \)

Correct Wrong

$$ \frac{7\tan45°}{\sin30°} $$

Correct Wrong

\( \tan60° \div \tan30° \)

Correct Wrong

\( 12( \sin45°)^2 \times ( \cos45°)^2 \)

Correct Wrong

$$ \left(\frac{5\sin60°}{\cos30°}\right)^2 $$

Correct Wrong

\(( \sin x°)^2 = 3( \cos 60°)^2 \)

\(x=\) Correct Wrong

\( \tan x° = \sin 60° \div \cos 30° \ \)

\(x=\) Correct Wrong

\( \sin x° + 1 = \tan 60° \times \cos 30° \)

\(x=\) Correct Wrong

\( \sin 45° \div \cos x° = 1\)

\(x=\) Correct Wrong

\( \cos x° = \tan 30° \times \sin 60° \)

\(x=\) Correct Wrong

\( 3\sin x° = 2\cos 30° \times \tan 60° \)

\(x=\) Correct Wrong

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Featured Activity

Hi-Low Predict

Hi-Low Predict

A version of the Play Your Cards Right TV programme. Calculate the probabilities of cards being higher or lower than the one shown. a fun way to practise applying probability and using fractions.

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Description of Levels

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Surds - Make sure you understand what surds are before starting the levels below.

Level 1 - Find exact trig values for special angles up to and including ninety degrees

Level 2 - Find the indicated lengths by solving trigonometric questions with exact solutions

Level 3 - Mixed questions on exact trig values of special angles up to and including ninety degrees

Level 4 - Find exact trig values for angles between ninety and three hundred and sixty degrees

Level 5 - Solving trigonometric equations with given domains

If Then - Find one trig ratio if given another from the same triangle.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Trigonometry including visual aids, investigations and self-marking exercises.

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Reminder Video

Helpful Diagrams

Common Trig Ratios
Trig Graphs

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