Everything Maths Grade 10

2.Ifsin=0,4 andis an obtuse angle, determine:

a) cos b)

p

21 tan

3.Giventan=

t

2

, where 0 ° 90 °. Determine the following in terms oft:

a) sec b) cot c) cos^2  d)tan^2 sec^2 

4.Given: 10 cos + 8 = 0and 180 ◦< < 360 ◦. Determine the value of:

a)cos

b)

3

tan

+ 2sin^2

5.Ifsin=

15

17

andcos < 0 find the following, without the use of a calculator:

a)cos

b)tan

c)cos^2 +sin^2 

6.Find the value ofsinA+cosAwithout using a calculator, given that 13 sinA12 = 0, wherecosA < 0.

7.If 17 cos= 8 andtan > 0 determine the following with the aid of a diagram (not a calculator):

a)

cos

sin

b) 17 sin 16 tan

8.Lis a point with co-ordinates(5; 8)on a Cartesian plane.LKforms an angle,, with the positivex-axis.
Set up a diagram and use it to answer the following questions.
a) Find the distanceLK. b)Determinesin.
c) Determinecos. d)Determinetan.
e) Determine cosec. f)Determinesec.
g) Determinecot. h) Determinesin^2 +cos^2 .

9.Given the following diagram and thatcos=^2425.

0

y

 x

A(a;b)

a)State two sets of possible values ofaandb.

b)IfOA= 100, state the values ofaandb.

c)Hence determine without the use of a calculator the value ofsin.

Chapter 5. Trigonometry 137