Understanding Engineering Mathematics

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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+


2

)
(v) cos

(
x+


2

)
(vi) tan

(
x+


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
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