# Exact trigonometry values

Some angles have neat values you can write without a calculator: sin 30 = 1/2, cos 60 = 1/2, tan 45 = 1.

Maths (school) · Part 06: Pythagoras and trigonometry · Card 6 of 9 · Last updated 2026-10-19

## Analogy

Like times tables for trigonometry: learn them once and use them again and again.

## Example

**Values to remember**

sin 30 = 1/2
cos 60 = 1/2
tan 45 = 1
sin 90 = 1, cos 0 = 1

## In practice

Non-calculator exams often ask for these exact values.

## Practice

### Flashcards

- **What is the exact value of sin 30?** 1/2.

## Questions people ask

### Why do sin 30 and cos 60 give the same value?

In a right-angled triangle with angles of 30 and 60 degrees, the side opposite 30 is the side next to 60. So sin 30 and cos 60 compare the same side to the hypotenuse. Both equal 1/2. The two angles add to 90, which is why sin of one equals cos of the other.

### How can you remember tan 45 = 1?

A right-angled triangle with a 45 degree angle also has another 45 degree angle, so it is isosceles. The opposite and adjacent sides are equal. Dividing equal sides gives 1, so tan 45 = 1. Picture a square cut along its diagonal, which makes two 45 degree triangles.

## Related concepts

- [Sine, cosine and tangent](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-3)
- [Finding a missing side](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-4)
- [Finding a missing angle](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-5)
- [Angles of elevation and depression](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-7)

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