Understanding Engineering Mathematics

(v) A= 40 °, b=5, c= 6

(vi) A= 120 °, b=3, c= 5

6.3.4 Graphs of trigonometric functions

➤➤

172 180

➤

Sketch the graphs of

(i) 2 sin

(

2 t+

π

3

)

(ii) 3 cos

(

3 t−

π

2

)

6.3.5 Inverse trigonometric functions

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172 184

➤

A.Find the principal value and general solutions for sin−^1 xand cos−^1 xfor the following
values:

(i) 0 (ii)

1

2

(iii) −

1

2

(iv)

√

3

2

(v)

1

√

2

(vi) −

1

√

2

B.Find the principal value and general solutions for tan−^1 xfor the following values ofx:

(i) 0 (ii) 1 (iii)

√

3(iv)−1(v)−

1

√

3

6.3.6 The Pythagorean identities – cos^2 Ysin^2 = 1

➤➤

172 185

➤

A.(i) Forc=cosθ, simplify

(a)

√

1 −c^2 (b)

c

√

1 −c^2

(c)

1 −c^2

c^2

(ii) Fors=sinθ, simplify

(a)

√

1 −s^2 (b)

√

1 −s^2

s^2

(c)

s

1 −s^2

(iii) Fort=tanθ, simplify

(a)

√

1 +t^2 (b)

t

( 1 +t^2 )

(c)

1

t

√

1 +t^2

B. Eliminateθfrom the equations

(i) x=acosθ, y=bsinθ (ii) x=asinθ, y=btanθ

C.For the following values of sinθ, find the corresponding values of cosθ and tanθ

without using your calculator, giving your answers in surd form, and assuming thatθ

is acute.

(i)

2

5

(ii)

1

13

(iii)

7

25