Angle of inclination

Definition

The angle of inclination θ satisfies m = tanθ, where m is the gradient. When the gradient is negative, add 180° so that 90° < θ < 180°.

Worked example

A line with m = 1 has θ = 45°; a line with m = −1 has θ = 135°.

The lines y = x and y = −x have inclinations 45° and 135°, so the angle between them is 135° − 45° = 90°.

Where it appears in the exam

Paper 2 analytical geometry asks for the angle of inclination of a line, or the angle between two lines, using tanθ = m.

Step-by-step method

1. Find the gradient m of the line.
2. Calculate θ = tan⁻¹(m).
3. If m is negative, add 180° to the calculator answer.
4. For the angle between two lines, subtract the smaller angle of inclination from the larger.

Common mistake

Giving a negative angle for a negative gradient instead of adding 180°.

Related analytical geometry terms

• Tangent to a circle

Frequently asked questions

What does angle of inclination mean in Grade 12 Maths?

The angle of inclination θ satisfies m = tanθ, where m is the gradient. When the gradient is negative, add 180° so that 90° < θ < 180°.

Which NSC paper tests angle of inclination?

Angle of inclination belongs to the Analytical geometry section of CAPS Grade 12 Mathematics, which is examined in Paper 2.

How do I practise questions involving angle of inclination?

Snap a question that uses angle of inclination into the Snap&Learn AI solver, or work through the analytical geometry topic guide and NSC past papers.