Calculators are essential for working with trigonometric functions — sine, cosine, and tangent — but correct results depend on mode, key entry, and interpretation. Trigonometry is used to find missing sides or angles in right-angled triangles.

Before using trig functions, always check the calculator is set to the correct angle mode. GCSE questions use degrees, not radians.

$$
\text{angle mode} = \text{degrees}
$$

To find a side when an angle and another side are known, use:

$$
\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}
$$

$$
\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}
$$

$$
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
$$

For example, to find the opposite side when the hypotenuse is \(10\) and the angle is \(30\):

$$
\sin 30 = \frac{x}{10}
$$

$$
x = 10 \times \sin 30
$$

$$
x = 5
$$

To find an angle, use the inverse trig functions (often labelled \(\sin^{-1}\), \(\cos^{-1}\), and \(\tan^{-1}\)).

For example, if the opposite side is \(6\) and the hypotenuse is \(10\):

$$
\sin \theta = \frac{6}{10}
$$

$$
\theta = \sin^{-1}(0.6)
$$

$$
\theta \approx 36.9
$$

Brackets are important when entering expressions involving trig functions.

$$
10 \times \sin(40)
$$

is not the same as:

$$
\sin(10 \times 40)
$$

Always round angles appropriately (usually to one decimal place unless stated otherwise), and check answers make sense by estimating. For example, a larger angle should correspond to a larger opposite side when the hypotenuse is fixed.

Topic Revision Checklist