Trigonometry
1) What is the size of Angle C?
- 40.5°
- 20.5°
- 10.5°
- 80.5°
Answer: 40.5°
2) If tan x + cot x = 2, find the value of tan²x + cot²x
- 4
- 8
- 5
- 2
Answer: 2
3) If sin x + cos x = √2sin (90 – x) determine cot x
- √2
- √2 + 1
- √2 - 2
- √2 + 2
Answer: √2 + 1
4) What is the size of Angle X?
- 44.9°
- 64.9°
- 47.9°
- 54.9°
Answer: 44.9°
5) If sin x = 3/5, find the values of tanx
- 4/3
- 2/3
- 7/3
- 3/4
Answer: 3/4
6) If cos x = 1/2, find the value of (2 secx / 1 + tan²x)
- 8
- 1
- 3
- 4
Answer: 1
7) Evaluate tan 35 × tan 60 × tan 55 × tan 30
- 1
- 7
- 4
- 2
Answer: 1
8) If cosec A = sec 25 find A
- 66
- 65
- 35
- 45
Answer: 65
9) If sin A = cos 33, find A
- 56
- 52
- 57
- 55
Answer: 57
10) Find the value of θ (0° ≤ θ ≤ 90°), when sin²θ - 3 sinθ + 2 = 0
- 0
- 30
- 55
- 90
Answer: 90
11) The diagram shows an arrowhead (re-entrant kite). Calculate the length of the side AB.
- 6.64 cm
- 9.64 cm
- 5.84 cm
- 5.64 cm
Answer: 5.64 cm
12) Farmer Jones has a triangular field ABC as shown in the following diagram: He wants to fence the field. Fencing is sold by the meter. How many meters of fencing does he need to purchase?
- 3,319.6 m
- 2,319.6 m
- 4,319.6 m
- 1,319.6 m
Answer: 1,319.6 m
13) If 3 tan θ = 4, evaluate (3sinθ + 2cosθ) / (3sinθ - 2cosθ)
- 9
- 6
- 5
- 3
Answer: 3
14) Express 1 + 2 sinA cosA as a perfect square.
- (sinA - cosA)²
- (cosA - sinA)²
- (cosA + sinA)²
- (sinA + cosA)²
Answer: (sinA + cosA)²
15) When A and B be acute angles, sin A = 0.3 and cos B = 0.7 it is
- Possible
- Data inadequate
- Impossible
- None of these
Answer: Possible
16) If 0° ≤ A ≤ 90° can sin A = 0.4 and cos A = 0.5 be
- Data inadequate
- None of these
- Impossible
- Possible
Answer: Impossible
17) Express in radians as well as in grades the fourth angle of a quadrilateral, which has three angles 46° 30' 10'', 75° 44' 45'', 123° 9' 35'' respectively.
- 5
- 7
- 2
- 9
Answer: 2
18) Convert the angle into centesimal system, (13751 / 120)°
- 117g 12` 41``
- 127g 32` 41``
- 147g 52` 41``
- 157g 32` 41``
Answer: 127g 32` 41``
19) Find the angle in radian through a pendulum swings if its length is 75cm and the tip describes an arc of length 10 cm
- 4/15
- 6/15
- 9/15
- 2/15
Answer: 2/15
20) Find the angle in radian through a pendulum swings if its length is 75cm and the tip describes an arc of length 15cm.
- 3 / 5
- 2 / 5
- 4 / 5
- 1 / 5
Answer: 1 / 5
21) Find the angle in radian through a pendulum swings if its length is 75cm and the tip describes an arc of length 21cm
- 8 / 25
- 6 / 25
- 7 / 25
- 8 / 15
Answer: 7 / 25
22) If G, D, denote respectively, the number of grades, degrees and radians in an angle then G/100 = D/90 =?
- 21
- 76
- 45
- 54
Answer: 21
23) If G, D, denote respectively, the number of grades, degrees and radians in an angle then G - D =?
- 350
- 346
- 201
- 654
Answer: 201
24) Large hand of a clock is 21cm long. How much distance does its extremity move in 20 minutes?
- 67
- 88
- 96
- 46
Answer: 88
25) Find the angle between the minute hand and hour hand of a click when the time is 7.20?
- 700⁰
- 800⁰
- 100⁰
- 500⁰
Answer: 100⁰
26) If tan = -2, find the values of the trigonometric ratios?
- 1 / 2
- -3 / 2
- -1 / 2
- 3 / 2
Answer: -1 / 2
27) Which of the following statement is correct for sin = x + 1/x is
- Not possible for real x
- Possible for real x
- Not possible for imaginary x
- Possible for imaginary x
Answer: Not possible for real x
28) Whether the equation 2 sin² - cos + 4 = 0 is
- Not possible
- None of these
- Possible
- Can’t determine
Answer: Not possible
29) Solve for a and c in the given triangle. Also find the area of the ABC.
- 783
- 183
- 683
- 283
Answer: 183
30) If A, B, A + B, A - B are positive acute angles, find the values of A and B from the equations: sin (A - B) = 1/2, cos (A + B) = 1/2
- (30, 25)
- (25, 10)
- (45, 15)
- (60, 15)
Answer: (45, 15)