 # Finding exact Trig Values

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Examples, solutions, and videos to help GCSE Maths students learn how to find the exact trigonometric values.

The following diagram shows how to use the CAST rule to help us see which quadrants the trig ratios are positive. Scroll down the page for more examples and solutions. How to find the exact trigonometric values: sin, cos, tan?
1. Draw the angle, look for the reference angle.
2. Use special triangles or the unit circle.
3. Check the quadrant to determine the sign (+ or -).

Trigonometry - Solving exact values of sin, cos, tan
Calculating exact values of sin, cos, tan without a calculator.
Example:
1. Calculate the exact value of cos (-π/2)
2. Calculate the exact value of sin (π/4)
3. Calculate the exact value of sin (π/6)
4. Calculate the exact value of sin (5π/3)
5. Calculate the exact value of cos (3π/4)
6. Calculate the exact value of tan 210°

Find exact trig values with CAST rule
How to use the trig. special triangles and CAST rule to determine the ratios associated with various angles?
Example:
Find the value of tan 314°
Find the value of cos 330°
Find Exact Values of Trig Functions
How to use the unit circle to find exact values of trigonometric functions?
Example:
Evaluate tan (-121π/4)
Evaluate sec (29π/6)

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  