Page 181 - Mathematics_Form_Two

Trigonometry

y

QUADRANT II QUADRANT I
Sine is positive Sine is positive
Cosine is negative Cosine is positive
FOR ONLINE READING ONLY
Tangent is negative Tangent is positive
QUADRANT III QUADRANT IV x
Sine is negative Sine is negative
Cosine is negative Cosine is positive
Tangent is positive Tangent is negative Mathematics for Secondary Schools

Figure 8�10: A reflex angle in a unit circle

The trigonometric ratios in the fourth Figure 8�11: Signs of trigonometric ratios
quadrant can be obtained by using the
sides of the right-angled triangle OQP as Example 8�11
follows: Write the signs of each of the following
trigonometrical ratios:
sinθ = (a) sin170° (c) tan310°

(b) cos240° (d) sin300°
cosθ Solution

(a) 170º lies in the second quadrant,
tanθ hence sin 170º is positive.

(b) 240º lies in the third quadrant,
Figure 8.10 shows that, the trigonometric hence cos 240º is negative.
ratios of sine and tangent in the fourth
quadrant are negative, while for the cosine is (c) 310º lies in the fourth quadrant,
positive as per corresponding x and y axes. hence tan 310º is negative.
(d) 300º lies in the fourth quadrant,
Signs of trigonometric ratios hence sin 300º is negative.

Trigonometric ratios can be positive or
negative depending on the size of the angle Example 8�12
or the quadrant in which the angle is found. Express each of the following in terms

The results obtained are summarised in of an acute angle:
Figure 8.11. These results are helpful in (a) cos165° (c) tan95°
determining whether sine, cosine, and
tangent of an angle is positive or negative. (b) sin317° (d) tan 258°

175
Student's Book Form Two

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MATHEMATIC F2 v5.indd 175 11/10/2024 20:14:00
MATHEMATIC F2 v5.indd 175