# The three trigonometric ratios

**The sine ratio**

The sine ratio is dependant on the size of the angles in the triangle. For example, what is the value of sin 65º?

In this example, the triangle is drawn to provide the opposite and hypotenuse.

sin 65º = opposite / hypotenuse

sin 65º = 10 / 11

sin 65º = 0.91 (to 2 d.p.)

**The sine ratio using a calculator**

If a scientific calculator is used to work out the sin 65°, the following is keyed in:

The answer should be 0.906 to 3 significant figures.

**The cosine ratio**

The value of the cosine ratio is dependent on the size of the angles in the triangle.

In the following example, the triangle is drawn to provide the opposite and hypotenuse.

cos 53º = adjacent / hypotenuse

cos 53º = 6 / 10

cos 53º = 0.60 (to 2 d.p.)

**The cosine ratio using a calculator**

If a scientific calculator is used to work out the cos 25°, the following is keyed in:

The answer should be 0.906 to 3 significant figures.

**The tangent ratio**

The value of the cosine ratio is dependent on the size of the angles in the triangle.

In the following example, the triangle is drawn to provide the opposite and hypotenuse.

tan 71º = opposite / adjacent

tan 71º = 11.6 / 4

tan 71º = 2.9

Point to note:

- Tangent ratio is different from sin and cos ratio as it is larger than 1.

**The tangent ratio using a calculator**

If a scientific calculator is used to work out the tan 71°, the following is keyed in:

The answer should be 2.90 to 3 significant figures.

**The relationship between sine and cosine**

Sin and Cos has similarities in that the sin of an angle is equal to the cos of the complement of that angle. Therefore:

sin 0 / cos (90 – 0)