Ratios and Graphs of Trigonometric Functions

Quadrant

One of the four regions of the coordinate plane, which decides the sign of a trigonometric ratio.

EnglishQuadrant
Bahasa MelayuSukuan
中文象限

How it is used

The angle 210° lies in the third quadrant. There only tangent is positive, so sin 210° = −sin 30° = −0.5, cos 210° = −cos 30° ≈ −0.866, and tan 210° = tan 30° ≈ 0.577.

Where it shows up in SPM

Quadrants appear in the Trigonometric Ratios chapter of Form 5. In Paper 1 you decide the sign of sin θ, cos θ or tan θ for an angle beyond 90°, and in Paper 2 you use the quadrant together with a reference angle to give an exact value or solve a trigonometric equation.

Don't confuse it with

Reference angleThe quadrant fixes the sign of the ratio, while the reference angle fixes its size; you need both to write the full value.
Quadrant of a circleHere a quadrant is one of four regions of the coordinate plane, not a quarter-circle sector used in area and perimeter work.

Open the chapter: Ratios and Graphs of Trigonometric Functions →

Frequently asked questions

How do I remember which ratios are positive in each quadrant?

Use the rule All, Sine, Tangent, Cosine going anticlockwise from the first quadrant. In the first all three are positive, in the second only sine, in the third only tangent, and in the fourth only cosine.

How do I find the reference angle in each quadrant?

The reference angle is the acute angle to the x-axis. In the second quadrant use 180° − θ, in the third θ − 180°, and in the fourth 360° − θ.

For 210° it is 210° − 180° = 30°, so the ratios use the value of 30°.

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