# Mathematics

## Mathematics

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...