Page 43 - CITS - WCS - Mechanical

WORKSHOP CALCULATION - CITS

Solution:
Given,
cos A = ⁴/5
As we know, from trigonometry identities,
1 + tan A = sec A
2
2
sec A – 1 = tan A
2
2
(1/cos A) -1 = tan A
2
2
Putting the value of cos A = ⁴/5.
(5/4)2 – 1 = tan A
2
(25 – 16)/16 = tan A
2
tan A = 9/16
2
tan A = 3/4.
2. If x sin θ + y cos θ = sin θ cos θ and x sin θ = y cos θ , then prove that x + y = 1.
3
3
2
2
3
3
3
xsin
θ

Solution: ycos 3 θ sinθ xsincosθ θ ycos θ sinθ cosθ
Solution
3
3 3
3
3 3

θ
cosθycosθ
θ xsin sinθθ
ycos
xsin xsin xsin 3 θ ycos 3 θ sinθ cosθ opp sinθ cosθ
θ ycosθ
cosθ
sinθ
3
tanθ
2
θ
3
xsin
ycos
3

sinθ
cosθ cos-(1 θ θs
ycos

θ)

yco xsins θ -(1 θ 3 θ cos 32 θ ycos ycoθ) sinθ sinθ cosθ adj cosθ ycos 3 θ sinθ cosθ
3
3

ycos

2 3
cosθ θycos
ycosθ ycos θ (1yco - θ (1 - cos 2 θ) ycos 3 θ 3 sinθ 600 3 sinθ cosθ
cos θs
θ ycos sinθ
θ) ycosθ ycos
sinθ cosθ
cosθ
θ
ycosθ
o
tan37
3

cosθ
ycosy

sinθy ycosθ ycos 3 θ 3 θ sinθ ycos 3 θ sinθ x y
ycosθ
θ

cosθ
sinθ
ycos
600
0.7536
y cosθx y sinθ x cosθ x y
sinθ
2
2
2 2
2
cos y)
LHS
x θn
x x cosθ y co LHS siθs 2 (0.7536)(x 2 θ 600 sin 2 θ 1 RHS
y RHS1
cosθ x
600
2
2
2
2
sin
2
LHS
RHS
cos
2
x
y
2
1
θ
θ
2
o
RHS
cos
θ
y
x
θ
sin 53 tan
LHS
1
3. An aeroplane is flying parallel to the Earth’s surface at a speed of 175 m/sec and at a height of 600 m. The
x
angle of elevation of the aeroplane from a point on the Earth’s surface is 37° at a given point. After what
600
x
period of time does the angle of elevation increase to 53°? (tan 53° = 1.3270, tan 37° = 0. 7536).
1.3270
x 452.15
Solution: 0.7536x 7536y 600
Solution
opp 0.7536 452.15 0.7536y 600
tanθ
adj
0.75.36y 600 340.74
tan37 o 600 0.7356y 259.26
x y
256.26
600 y
0.7536 0.7356
x y
y 344.03
(0.7536)(x y) 600
Distance 344.03
tan 53 o 600 Time speed 344.03
x
600 344.03 344.03
x Time 1.97sec
1.3270 speed 175
x 452.15 Time 1.97sec
0.7536x 7536y 600
0.7536 452.15 0.7536y 600
0.75.36y 600 340.74
0.7356y 259.26
256.26
y
0.7356
y 344.03
Distance 344.03 30
Time speed 344.03 CITS : WCS - Mechanical - Exercise 6
344.03 344.03
Time 1.97sec
speed 175
Time 1.97sec