Page 33 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
5 Mathematics Chapter 6 Ratios and Graphs of Trigonometric Functions

6.1 The Value of Sine, Cosine and (b) y
Tangent for Angle θ,
0° < θ < 360° 140° 140° lies in
x quadrant II.
O
Make and verify conjecture about the
value of sine, cosine and tangent for
angles in quadrants II, III and IV with the (c) y
corresponding reference angle
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1. A Cartesian plane is divided into four parts 230° 230° lies in
(called quadrant) by the x-axis and the y-axis. O x quadrant III.
The quadrants are named as quadrant I,
quadrant II, quadrant III and quadrant IV in the
anticlockwise direction. y
y (d)
90°
310° lies in
310° quadrant IV.
Quadrant Quadrant O x
II I
0°
x
O
180° 360°
Quadrant Quadrant
III IV Try question 1 in Formative Zone 6.1
270°
3. y
2. y
P(x, y)
P 1 y
θ x
θ O x Q
x
O

PQ y
sin θ = —–— = —– = y
1
OP
CHAP. An angle θ is measured by rotating the line OP ∴ sin θ = y-coordinate
6 in the anticlockwise direction from the positive OQ x
x-axis at the origin. cos θ = —–— = —– = x
OP 1
∴ cos θ = x-coordinate
Example 1 y
PQ
tan θ = —–— = —–
Sketch on separate diagrams to represent the OQ x
angles (a) 50°, (b) 140°, (c) 230° and (d) 310°. y-coordinate
Hence, determine the quadrant for each of the ∴ tan θ = —–—————
x-coordinate
angles lies.
Solution: BRILLIANT Tips
(a) y BC
C • sin θ = —––
Hypotenuse AC
AB
50° lies in Opposite side • cos θ = —––
50° quadrant I. θ AC
BC
O x • tan θ = —––
A B AB
Adjacent side

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