Understanding Engineering Mathematics

6.3 Reinforcement

6.3.1 Radian measure and the circle

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A.Express as radians:

(i) 36° (ii) 101° (iii) 120° (iv) 250°

(v) 340° (vi) − 45 ° (vii) − 110 ° (viii) 15°

(ix) 27° (x) 273°

B. Express the following radian measures in degrees in the range 0°≤θ< 360 °.

(i)

2 π

3

(ii) 14π (iii) −

π

2

(iv)

π

3

(v)

π

6

(vi)

5 π

2

(vii)

2 π

9

(viii)

5 π

4

(ix) −

2 π

5

(x)

π

12

C.Determine the length of arc and the area of the sector subtended by the following
angles in a circle of radius 4 cm.

(i) 15° (ii) 30° (iii) 45° (iv) 60°

(v) 90° (vi) 120° (vii) 160° (viii) 180°

6.3.2 Definitions of the trig ratios

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A.Write down the exact values of sine, tan, sec, and complementary ratios for all ‘special’
angles 0,π/2,π/3,π/4,π/6.

B. Classify as odd or even functions: cos, sin, tan, sec, cosec, cot.

C.Express as trig functions ofx(nis an integer):

(i) sin(x+nπ) (ii) cos(x+nπ) (iii) tan(x+nπ)

(iv) sin

(

x+

nπ

2

)

(v) cos

(

x+

nπ

2

)

(vi) tan

(

x+

nπ

2

)

wherenis an integer.

6.3.3 Sine and cosine rules and the solution of triangles

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With the standard notation solve the following triangles.

(i) A= 70 °, C= 60 °, b= 6

(ii) B= 40 °, b=8, c= 10

(iii) A= 40 °, a=5, c= 2

(iv) a= 5 b=6, c= 7