Page 197 - Mathematics_Form_Two

Trigonometry

Chapter summary 4. Angle of elevation and depression:

1. Trigonometric ratios (a) Angle of elevation is the angle
Length of opposite side to angle A obtained when the line of sight
sin A = is above a horizontal line.
Length of hypotenuse side
Length of adjacent side to angle A (b) Angle of depression is the
cos A = Length of hypotenuse side angle is obtained when the line
cosα FOR ONLINE READING ONLY
Length of opposite side to angle A of sight is below a horizontal
tan A = Length of adjacent side to angle A line.

2. Trigonometric ratios for special Revision exercise 8 Mathematics for Secondary Schools
angles: 1. Use a calculator to find each of the

x sin x cos x tan x following:

0º 0 1 0 (a) sin 60º
(b) cos 28º 28′

30º 1 3 3 (c) tan 63º 48′
2 2 3 2. Use a calculator to find the value of y
in each of the following:
2 2
45º 1 (a) tan y = 0.9036
2 2
(b) cos y = 0.2554
3 1
60º 3 (c) sin y = 0.4971
2 2
90º 1 0 undefined 3. In the following figure, find the
values of a and .x
180º 0 −1 0

270º −1 0 undefined
360º 0 1 0 a°

3. Relationship between trigonometric
ratios for angle ∝.

(a) sinα cos(90°− α = )
(b) sin(90°− α = )
sinα
(c) tanα =
cosα 4. A pendulum bob is hanging at the
(d) sin α 2 cos α + 2 = 1 end of a string which is 18 cm long.
(e) sin( α − ) = − sinα Find the vertical height through which
(f) cos( α − ) cosα = the bob rises and falls as the pendulum

(g) tan( α − ) = − tanα swings through 30° in each side of the
vertical.

191
Student's Book Form Two

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MATHEMATIC F2 v5.indd 191