Trigonometry basic, Geometry basic - Question Bank

1. If sin(θ) = 3/5, what is the value of cos(θ) in a right-angled triangle where θ is acute?
A) 4/5
B) 5/4
C) 3/5
D) 5/3
2. In a right-angled triangle, the sides are in the ratio 3:4:5. If the smallest side is 6 cm, what is the length of the hypotenuse?
A) 8 cm
B) 10 cm
C) 12 cm
D) 15 cm
3. What is the value of tan(360°)?
A) 0
B) 1
C) -1
D) Undefined
4. What is the value of cos(360°)?
A) 0
B) 1
C) -1
D) Undefined
5. What is the value of sin(360°)?
A) 0
B) 1
C) -1
D) Undefined
6. What is the value of tan(270°)?
A) 0
B) 1
C) -1
D) Undefined
7. What is the value of cos(270°)?
A) 0
B) 1
C) -1
D) Undefined
8. What is the value of sin(270°)?
A) 0
B) 1
C) -1
D) Undefined
9. What is the value of tan(180°)?
A) 0
B) 1
C) -1
D) Undefined
10. In a triangle, if a line is drawn parallel to one side, it divides the other two sides proportionally. This is the:
A) Pythagorean Theorem
B) Basic Proportionality Theorem
C) Sine Rule
D) Cosine Rule
11. The ratio of the side adjacent to an angle to the hypotenuse in a right-angled triangle is:
A) Sine
B) Cosine
C) Tangent
D) Cosecant
12. What is the value of cos(180°)?
A) -1
B) 0
C) 1
D) Undefined
13. If a triangle has one angle greater than 90 degrees, it is called a(n):
A) Acute triangle
B) Right-angled triangle
C) Obtuse triangle
D) Scalene triangle
14. What is the value of sin(180°)?
A) 0
B) 1/2
C) 1
D) Undefined
15. The identity 1 + tan²θ = sec²θ is derived from which fundamental identity?
A) sin²θ + cos²θ = 1
B) sinθ = cos(90° - θ)
C) tanθ = sinθ/cosθ
D) cotθ = cosθ/sinθ
16. In a circle, a radius is a line segment connecting the center to:
A) Another point on the circumference
B) The center of the circle
C) A point outside the circle
D) The diameter
17. What is the value of tan(90°)?
A) 0
B) 1
C) √3
D) Undefined
18. If a triangle has all angles less than 90 degrees, it is called a(n):
A) Right-angled triangle
B) Obtuse triangle
C) Acute triangle
D) Isosceles triangle
19. What is the value of cos(45°)?
A) 1/2
B) 1/√2
C) √3/2
D) 1
20. In any triangle ABC, the sine rule states that a/sin(A) = b/sin(B) = c/sin(C) is equal to:
A) 2R (where R is the circumradius)
B) R
C) R/2
D) 1/R
21. Which trigonometric ratio is the reciprocal of cosine?
A) Sine
B) Tangent
C) Cotangent
D) Secant
22. What is the value of sin(45°)?
A) 1/2
B) 1/√2
C) √3/2
D) 1
23. If an angle in a triangle is 90 degrees, it is called a:
A) Acute triangle
B) Obtuse triangle
C) Right-angled triangle
D) Equilateral triangle
24. What is the value of cos(30°)?
A) 1/2
B) √3/2
C) 1
D) 0
25. In a circle, the angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the:
A) Circumference
B) Diameter
C) Radius
D) Chord
26. Which trigonometric ratio is the reciprocal of tangent?
A) Sine
B) Cosine
C) Cotangent
D) Cosecant
27. What is the value of sin(60°)?
A) 1/2
B) √3/2
C) 1
D) 0
28. If two lines intersect, the vertically opposite angles are:
A) Always equal
B) Always supplementary
C) Always complementary
D) Never equal
29. What is the value of tan(30°)?
A) 1/2
B) 1/√3
C) √3
D) 1
30. In a triangle, if two sides are equal, then the angles opposite to these sides are:
A) Different
B) Equal
C) Supplementary
D) Complementary
31. What is the value of cos(60°)?
A) 1/2
B) √3/2
C) 1
D) 0
32. Which trigonometric ratio is the reciprocal of sine?
A) Cosine
B) Tangent
C) Secant
D) Cosecant
33. What is the value of sin(30°)?
A) 1/2
B) √3/2
C) 1
D) 0
34. If a chord of a circle subtends an angle of 90° at the center, it is:
A) A radius
B) A diameter
C) A tangent
D) A secant
35. What is the value of tan(60°)?
A) 1/√3
B) 1
C) √3
D) 2
36. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to:
A) The sum of the squares of the other two sides
B) The difference of the squares of the other two sides
C) The product of the other two sides
D) The square of one of the other sides
37. What is the value of cos(0°)?
A) 0
B) 1/2
C) 1
D) Undefined
38. In a parallelogram, opposite angles are:
A) Always equal
B) Always supplementary
C) Always complementary
D) Never equal
39. What is the value of sin(90°)?
A) 0
B) 1/2
C) 1
D) √3/2
40. What is the area of a triangle with base 'b' and height 'h'?
A) b * h
B) 1/2 * b * h
C) b + h
D) 2 * b * h
41. If the angle of elevation of the sun is 45°, what is the ratio of the height of a vertical object to its shadow length?
A) 1:1
B) 1:√3
C) √3:1
D) 2:1
42. What is the fundamental trigonometric identity relating sine and cosine?
A) sin²θ + cos²θ = 1
B) tan²θ + 1 = sec²θ
C) 1 + cot²θ = csc²θ
D) sinθ = cos(90° - θ)
43. In a circle, a diameter divides the circle into how many equal parts?
A) Two semicircles
B) Four quadrants
C) Six sectors
D) Eight segments
44. What is the value of tan(45°)?
A) 0
B) 1/2
C) 1
D) √3
45. If two parallel lines are intersected by a transversal, the alternate interior angles are:
A) Equal
B) Supplementary
C) Complementary
D) None of the above
46. What is the ratio of the side opposite to an angle to the hypotenuse in a right-angled triangle?
A) Cosine
B) Tangent
C) Sine
D) Cotangent
47. The sum of the interior angles of a triangle is always:
A) 90 degrees
B) 180 degrees
C) 270 degrees
D) 360 degrees
48. What is the value of cos(90°)?
A) 0
B) 1/2
C) 1
D) Undefined
49. If a triangle has sides of length 3, 4, and 5 units, what type of triangle is it?
A) Equilateral
B) Isosceles
C) Scalene
D) Right-angled
50. What is the value of sin(0°)?
A) 0
B) 1/2
C) 1
D) Undefined
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