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Common Trig Ratios :: Degrees

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

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Solve these trigonometric equations to find the solution in the given domain. Non exact answers should be given to three significant figures.

\( \tan(x) = 1\\ 90° \lt x \lt 270° \)

\(x=\) ° Correct Wrong

\( \sin(x) = 0.5\\ 90° \lt x \lt 180° \)

\(x=\) ° Correct Wrong

\( x = \cos^{-1}(0.5)\\ -90° \lt x \lt 0° \)

\(x=\) ° Correct Wrong

\( x = \tan^{-1}(0)\\ 90° \lt x \lt 270° \)

\(x=\) ° Correct Wrong

\( \cos(x) = \frac{ \sqrt{3}}{2} \\ 0° \lt x \lt 270° \)

\(x=\) ° Correct Wrong

\( \sin(x) = \frac{ \sqrt{3}}{2} \\ 90° \lt x \lt 180° \)

\(x=\) ° Correct Wrong

\( 5\tan(x) - 3 = 1 + 2\tan(x) \\ -90° \lt x \lt 90° \)

\(x=\) ° Correct Wrong

\( 5\cos(x) - 2 = \frac{1}{3} \\ -180° \lt x \lt 0° \)

\(x=\) ° Correct Wrong

\( 2(3\sin(x) - 1) = \frac{1}{4}\\ 450° \lt x \lt 540° \)

\(x=\) ° Correct Wrong

\( 7\tan(x) + 4 = 5\tan(x) \\ 180° \lt x \lt 360° \)

\(x=\) ° Correct Wrong

\( \frac{6}{\cos(x)} = 10\\ 180° \lt x \lt 360° \)

\(x=\) ° Correct Wrong

\( 2\sin(x) + 1 = 2.1\\ 360° \lt x \lt 450° \)

\(x=\) ° Correct Wrong

\( \frac{5}{\sin(2x)} = 8\\ -45° \lt x \lt 45° \)

\(x=\) ° Correct Wrong

\( \tan^2(3x) = 5\\ 100° \lt x \lt 150° \)

\(x=\) ° Correct Wrong

\( 6\cos^2(x) = 1 - \cos(x) \\ -180° \lt x \lt -90° \)

\(x=\) ° Correct Wrong

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Instructions

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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

Radians - A similar set of exercises worked in radians.

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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