If Then Trigonometry

Finding the exact values of sine, cosine and tangent of angles if given a different trig ratio.

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Solve these "If Then" questions without using a calculator but giving exact answers in their simplest form. Use the / symbol to show a fraction and the root button to insert the square root sign if required.

 If $$\tan \theta = \frac{3}{4}$$then find $$\sin \theta$$ If $$\cos \theta = \frac{12}{13}$$then find $$\tan \theta$$ If $$\sin \theta = \frac{3}{5}$$then find $$\cos \theta$$ If $$5\sin \theta = 4$$then find $$\tan \theta$$ If $$3\tan \theta = 4$$then find $$\cos \theta$$ If $$13\cos \theta = 5$$then find $$\sin \theta$$ If $$2\sin \theta = \sqrt{3}$$then find $$\cos \theta$$ If $$2\cos \theta = 1$$then find $$\tan \theta$$ If $$\tan \theta = 1$$then find $$\sin \theta$$
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Description of Levels

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

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

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

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

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

Common Trig Ratios Level 5 - Solving trigonometric equations with given domains

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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Help

The questions in this exercise are designed to be solved by drawing a diagram of a right-angled triangle, choosing the lenghts of two of the sides using the given ratio then use Pythagoras' theorem to figure out the length of the third side. The required trig ratio can then be found from the diagram.

For example, if $$\tan \theta = \frac{8}{15}$$ then find $$\sin \theta$$

Firstly sketch a righ-angled triangle containing the angle $$\theta$$, opposite 8 and adjacent 15.

The length of the hypotenuse can be calculated using pythagoras' Theorem to be $$\sqrt{8^2 + 15^2} = 17$$.

Finally $$\sin \theta$$ can be calculated as the opposite over the hypotenuse which is $$\frac{8}{17}$$.