Understanding Engineering Mathematics

seen that

sinα=cosβ=cos( 90 °−α)

cosα=sinβ=sin( 90 °−α)

tanα=cotβ=cot( 90 °−α)

cotα=tanβ=tan( 90 °−α)

i.e. the ‘co-trig ratio’ is the ratio of the complementary angle.

Solution to review question 6.1.2

Youwillfinditveryusefultocommitasmanyoftheseaspossibleto

memory. Many of these results can be obtained from Figure 6.4.

(i) cos 0= 1

(ii) cos 2π= 1

(iii) sin 90°= 1

(iv) sin

π

4

=

1

√

2

(this is theexactvalue – see Figure 6.4)

(v) cos

π

2

= 0

(vi) sin 45°=sin

π

4

=

1

√

2

(vii) tan 90°is, strictly, not defined but it is usual to take it as∞

(viii) sin 0= 0

(ix) sin 60°=

√

3

2

(x) sin

2 π

3

=sin

π

3

=

√

3

2

(xi) cos

π

3

=

1

2

(xii) tan 45°= 1

(xiii) cos 30°=

√

3

2

(xiv) sin 30°=

1

2

(xv) tan

π

3

=

√

3

(xvi) cos 45°=

1

√

2

(xvii) cos

3 π

2

=cos

π

2

= 0

(xviii) tan(− 60 °)=−tan 60°=−

√

3

(xix) sin(− 120 °)=−sin 120°=−

√

3

2