Page 180 - Mathematics_Form_Two

Trigonometry

Figure 8.7 shows that all the trigonometric In Figure 8.9, θ is a reflex angle
ratios are positive as per corresponding x (180º < θ < 270º), which is in the third
and y axes. quadrant.

In Figure 8.8, θ is an obtuse angle
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(90º < θ < 180º) located in the second
Mathematics for Secondary Schools angle 180º – θ.
quadrant. The trigonometric ratios of θ are
related to the trigonometric ratios of acute

Figure 8�9: Reflex angle in a unit circle

The trigonometric ratios of θ are related to
the trigonometric ratios of an acute angle
θ – 180º. The trigonometric ratios in the
third quadrant can be obtained by using
the sides of the right-angled triangle OQP
as follows:
Figure 8�8: Reflex angle in a unit circle

The trigonometric ratios in the second sinθ =
quadrant can be obtained by using the
sides of a right-angled triangle OQP as cosθ

follows:
tanθ
QP y
sinθ = = y = sin(180 θ = − )
OP 1
Figure 8.9 shows that, the trigonometric
QP −x
cosθ = = =−x =−cos(180−θ) ratios of sine and cosine in the third
OP 1 quandrant are negative, while for the
QP y tangent is positive as per corresponding x
tanθ = = =−tan(180−θ) and y axes.
OQ −x

From Figure 8.8, it can be observed that, In Figure 8.10, θ is a reflex angle
the trigonometric ratio of sine in the (270°< θ<360°) which is in fourth
seocond quadrant is positive, while those quadrant. The trigonometric ratios of θ
of cosine and tangent are negative as per are linked to the trigonometric ratios of an

corresponding x and y axes. acute angle 360º – θ.

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 174 11/10/2024 20:13:59