8/10/2019 Solomon question paper C3 topic

1/2

Solomon Press

TRIGONOMETRYC3 Worksheet A

1 Find to 2 decimal places the value of

a sec 23 b cosec 185 c cot 251.9 d sec (302)

2 Find the exact value of

a cosec 30 b cot 45 c sec 150 d cosec 300

e cot 90 f sec 225 g cosec 270 h cot 330

i sec 660 j cosec (45) k cot (240) l sec (315)

3 Find to 2 decimal places the value of

a cot 0.56c b cosec 1.74

c c sec (2.07

c) d cot 9.8

c

4 Find in exact form, with a rational denominator, the value ofa sec 0 b cosec

4 c cot 3

4 d sec 4

3

e cosec 23

f cot 72

g sec 54

h cosec 56

( )

i cot 116

j sec (4) k cosec 134

l cot 73

( )

5 Given that sinx= 45

and that 0

8/10/2019 Solomon question paper C3 topic

2/2

Solomon Press

10 Solve each equation forxin the interval 0 x2, giving your answers in terms of .

a cotx= 1 b secx= 2 c cosecx= 2 d cotx= 0

e secx= 1 f cosecx= 2 g cotx= 3 h secx= 2

11 Solve each equation for in the interval 0 360, giving your answers to 1 decimal place.

a sec = 1.8 b cosec = 2.57 c cot = 1.06 d sec = 2.63

e cosec = 3 f cot = 0.94 g sec = 1.888 h cosec = 1.2

12 Solve each equation forxin the interval 180 x180

Give your answers to 1 decimal place where appropriate

a cosec (x+ 30)= 2 b cot (x57)= 1.6 c sec 2x= 2.35

d 5 2cotx= 0 e 3 sec (x60)= 2 f 2cosec 12x7 = 0

g sec (2x18)= 1.3 h cosec 3x= 3.4 i cot (2x+ 135)= 1

13 Solve each equation for in the interval 0 360.

Give your answers to 1 decimal place where appropriate.

a cosec24 = 0 b sec

22sec 3 = 0

c cot cosec = 6cot d cosec = 4sec

e 2cos = cot f 5sin 2cosec = 3

14 Solve each equation forxin the interval

x

.Give your answers to 2 decimal places.

a 2cosec2x+ 5cosecx12 = 0 b secx= 3tanx

c 3secx= 2cotx d 4 + tanx= 5cotx

e cosecx+ 5cotx= 0 f 6tanx 5cosecx= 0

15 Prove each identity.

a secxcosxsinxtanx b (1 + cosx)(cosecxcotx) sinx

ccot cos

1 sin

x x

cotx d (sinx+ tanx)(cosx+ cotx) (1 + sinx)(1 + cosx)

16 y

O x

y= f(x)

The diagram shows the curve y= f(x), where

f(x) 2 cosx3 secx5, x , 0 x2.

a Find the coordinates of the point where the curve meets they-axis.

b Find the coordinates of the points where the curve crosses thex-axis.

C3 TRIGONOMETRY Worksheet A continued