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...