- Submitted By: 韩-彬
- Date Submitted: 07/08/2016 2:33 AM
- Category: Technology
- Words: 1097
- Page: 5

FHMM1014 MATHEMATICS 1

TUTORIAL 4 TRIGONOMETRY

1.

Evaluate the expression without using a calculator.

(a) sin cos

(b) sin 30 cos 60 sin 60 cos 30

6

6

(c) (cos 30) 2 (sin 30) 2

2.

Find the exact value of the trigonometric function.

(a) sin 150

(f) sec

(b) tan( 60)

(c) cos 570

(d) sin

3

2

17

3

7

(e) cos

3

3.

Find the area of a triangle with sides of length 10 and 22 and included angle 10 .

4.

A triangle has an area of 16 cm2 , and two of the sides of triangle have lengths 5

cm. and 7 cm. Find the angle included by these two sides.

5.

Given A 52 , B 70 , c 26.7 . Find the side a.

6.

Given A 46 , B 20 , c 65 . Solve the triangle.

7.

Given B 29 , C 51 , b 44 . Solve the triangle.

8.

Use the Law of Sines to solve for all possible triangles that satisfy the given

conditions.

(a) a 20, c 45, A 125

(b) a 26, c 15, C 29

9.

The Leaning Tower of Pisa, leans 5.6 from the vertical. A tourist stands 105m

from its base, with the tower leaning directly toward her. She measures the angle

of elevation to the top of the tower to be 29.2 . Find the length of the tower.

10.

Solve the following triangles

(a) a 18 , b 10 , C 120 .

(b) a 20 , b 25 , c 22

11.

Find the area of the triangle whose sides have the given lengths.

(a) a 9 , b 12 , c 15

(b) a 7 , b 8 , c 9

12.

Write

sec cos

in terms of sine and cosine, and then simplify.

sin

1

FHMM1014 MATHEMATICS 1

2 tan 2 x

1.

sec 2 x

13.

Simplify

14.

Verify the identity

(a) sin B cos B cot B csc B

sec t cos t

sin 2 t

(b)

sec t

(sin t cos t ) 2

(c)

2 sec t csc t

sin t cos t

(d) (tan x cot x) 4 csc 4 x sec 4 x

15.

Use an addition or subtraction formula to find the exact value of the expression.

(a) sin 15

(b) tan

12

16.

Use...