Understanding Engineering Mathematics

(x) sin

2 π

3

(xi) cos

π

3

(xii) tan 45°

(xiii) cos 30° (xiv) sin 30° (xv) tan

π

3

(xvi) cos 45° (xvii) cos

3 π

2

(xviii) tan(− 60 °)

(xix) sin(− 120 °) (xx) cos

(

−

π

3

)

(xxi) sin( 585 °)

(xxii) cos( 225 °) (xxiii) tan(− 135 °) (xxiv) sec 30°

(xxv) cosecπ/ 4 (xxvi) cot 60° (xxvii) sec 120°

(xxviii) cos

(

−

π

2

)

(xxix) cosec(− 60 °)

6.1.3 Sine and cosine rules and solutions of triangles ➤178 194➤➤

For the triangle below find (i)a (ii)θ.

a

2

5

q

60 °

6.1.4 Graphs of the trigonometric functions ➤180 195➤➤

Sketch the graphs of (i) 3 sin

(

t−

π

2

)

(ii) 4 cos

(

2 t−

π

6

)

(iii) tan

(

t+

π

2

)

6.1.5 Inverse trigonometric functions ➤184 195➤➤

Evaluate the following inverse trigonometric ratios in the range 0≤θ≤ 90 °:

(i) sin−^1

(

1

2

)

(ii) sin−^1

(√

3

2

)

(iii) cos−^1

(√

3

2

)

(iv) cos−^1

(

1

2

)

(v) tan−^1

(

1

√

3

)

(vi) tan−^1 (

√

3 )

6.1.6 The Pythagorean identities – cos^2 Ysin
2
= 1 ➤185 195➤➤

Complete the following table in which each angle is in the first quadrant:

sinθ cosθ tanθ

(i)

1

7

(ii)

1

√

3

(iii)

1

√

2