Introduction to Trigonometic Ratios

Learning Objectives
1 understand cosine, sine and tangent of acute angles
2 apply trigonometric ratios on simple problems

Title page story, oral and dictation
There is a frog staying at the base of a cylindrical well with the depth of 10 m and base radius of 2 m. Every night, the frog looks at the moon at the centre of the well. Without taking the height of the frog into account and assume it will not climb up the well, at where, the centre or edge of the base, can the frog obtain a
larger angle of view 0?(theta)

also theta, alpha, beta, phi

Hints
1 Draw the possible angles of view of the frog when it is at the centre and at the edge of the base of the well.
2 At where, the centre or edge of the base, can the frog see more? Explain briefly.

Preview
abbreviation, corresponding
Pythagoras' theorem

11.1 Cosine Ratio of an Angle, Origin of trigonometry
11.2 Sine Ratio of an Angle
11.3 Tangent Ratio of an Angle
11.4 Applications of Trigonometric Ratios
11.5 Properties of Trigonometric Ratios

11.1 Cosine Ratio of an Angle
Mr. Lam is planning to put up a ribbon of coloured flags from the ground toen the top floor of the school building. It is known that the angle made by the ribbon with
the ground is 25, and the ribbon attached to the ground is 32 m away from the school
building. Can you estimate the length of the ribbon?

A Meaning of cosine
hypotenuse, opposite side, adjacent side
**cosine ratio: adjacent side/hypotenuse
Finding cosine ratio with the sides given
Finding the adjacent side with the cosine ratio given
Finding the hypotenuse with the cosine ratio given

B Origin of trigonometry
trigonometric ratios
trigonometry meanings surveying and triangle
architecture, surveying, engineering and sailing.

level 2
1 horizontal distance travelled by the car
2 the distance between the foot of the ladder and the bottom of the wall
3 the kite and the length of the string
4 diagonal and the dimensions of the field

C Use of calculators
CASIO fx-3650p/fx-3950p

D Finding angles through cosine ratios

**Chapter Summary
Hypotenuse, Opposite side, Adjacent side

Additional Questions
2 Mr. Chan lives in a 3-storey house. At a distance of 1.5 m from the house, there is a lamp post. During a windstorm yesterday, the lamp post fell and leaned against
his house with its top locating above the roof. at noon, the lamp post casts a
shadow of 0.5 m long on the roof. Mr. Chan is going to claim the damage from an
insurance company. Can you help him solve the following problems for his insurance
claim?

Repeat and check carefully again