Read sine, cosine and tangent graphs in degrees

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Read sine, cosine and tangent graphs in degrees

Sine and cosine repeat every 360° and have outputs between −1 and 1. Over one cycle, sine has zeros at 0°, 180° and 360°, a maximum at 90° and a minimum at 270°. Cosine starts at 1, reaches zero at 90° and 270°, and reaches −1 at 180°.

Tangent is different: it repeats every 180° and has no finite upper or lower output bound. It is undefined at 90° + 180°n for integer n, where the graph has vertical asymptotes. Its zeros occur at multiples of 180°.

The angle unit is part of the calculation. Use degree mode for this GCSE graph interpretation. Never connect a tangent branch across an asymptote, and do not copy the sine amplitude restriction onto tangent.

Worked example: Read sin 90°, cos 180° and tan 0°.

Identify the maximum of sine.

Identify the minimum of cosine.

Use the tangent zero at the origin.

Answer: 1, −1 and 0.

Check your understanding: Is tan 90° equal to 1?

Answer: No; it is undefined.

Why: Cosine is zero there, so sin x / cos x cannot be evaluated.