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Exact trigonometric values
You must know some sin, cos and tan values without a calculator. Two special triangles let you work them out.
The values
Where they come from
Half of an equilateral triangle with sides 2 gives a 30°, 60°, 90° triangle with sides 1, √3, 2.
A right-angled isosceles triangle with short sides 1 has hypotenuse √2, giving the 45° values.
A right-angled isosceles triangle with short sides 1 has hypotenuse √2, giving the 45° values.
Patterns to remember
sin goes 0, 12, √22, √32, 1. cos is the same list backwards.
tan 45° = 1 because the opposite and adjacent sides are equal.
tan 45° = 1 because the opposite and adjacent sides are equal.
Without a calculator, find the opposite side when the hypotenuse is 10 and the angle is 30°.
- sin 30° = 12
- opposite = 10 × 12
Answer: 5
Learn sin and cos of 0°, 30°, 45°, 60° and 90° (cos is sin backwards), and tan 0° = 0, tan 45° = 1. They come from two special triangles.
The interactive lesson includes the diagrams for this topic.
Check you have got it
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