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Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 3)

1
Which trigonometric ratio is the reciprocal of cosine?
Answer
(B)
Secant
2
If the cosine of an angle is 0.8, what is the ratio of the adjacent side to the hypotenuse?
Answer
(C)
0.8
3
If in a right-angled triangle, which ratio applies?
Answer
(D)
all the above
4
In a right-angled triangle, what is the side directly across from the right angle called?
Answer
(C)
Hypotenuse
5
Which of the following statements is true about bearings?
Answer
(C)
Bearings are measured clockwise from the north.
6
If an angle of elevation is 30 degrees, what is the angle of depression from the same point?
Answer
(A)
30 degrees
7
For the area of any triangle, which of the following formulas is/are valid?
Answer
A
B
8
What is the area of a triangle with base 6 cm and height 4 cm?
Answer
(C)
12 cm^2
9
If sin(x) = 0.707, what is the value of x (in degrees)?
Answer
(B)
45 degrees
10
In trigonometry, what does 'adjacent' refer to in relation to an angle in a right triangle?
Answer
(B)
The side next to the angle, not the hypotenuse
11
If the sine of an angle is 0.5, what is the angle?
Answer
(A)
30 degrees
12
The angle of elevation of a point B from point A is the angle between the horizontal plane and:
Answer
(B)
A line of sight above the horizontal plane
13
If the hypotenuse of a right triangle is 10 cm and one angle is 60 degrees, what is the length of the side opposite the 60-degree angle?
Answer
(B)
8.66 cm
14
Which of the following represents the correct formula for the Pythagorean theorem?
Answer
(B)
a^2 + b^2 = c^2
15
Which trigonometric ratio is defined as Opposite/Adjacent?
Answer
(C)
Tangent
16
In the ambiguous case of the sine rule, if the given angle is obtuse, how many possible triangles are there?
Answer
(B)
1
17
What is the relationship between sine and cosine in the context of a right-angled triangle?
Answer
(C)
Sine of an angle equals cosine of its complement.
18
If you have a right triangle with sides of length 3 and 4, what is the length of the hypotenuse?
Answer
(B)
5
19
If you know two sides and the angle between them in a triangle, which is the best method to find the area?
Answer
(B)
Area = 1/2 * ab * sinC
20
In the context of trigonometry, what are the core elements required to solve for unknown sides or angles in right triangles?
Answer
A
B
D
21
What is the value of tan(45°)?
Answer
(B)
1
22
Which of the following is NOT a trigonometric ratio?
Answer
(D)
Area
23
Which of the following formulas is a correct representation of the Pythagorean theorem?
Answer
A
B
D
24
If in a parallelogram, the area is to be calculated from two adjacent sides, which function will be needed?
Answer
(A)
sin
25
In a 3D context, what is the method to find the lengths and angles of three-dimensional objects?
Answer
(D)
All of the above
26
What is the period of the sine function?
Answer
(C)
2π
27
Which of the following are necessary to apply the sine rule?
Answer
A
C
28
If the length of the adjacent side to a 30-degree angle is 5, what is the approximate length of the hypotenuse?
Answer
(A)
2.5
29
What is sin(180°) equal to?
Answer
(A)
0
30
What does 'bearing' refer to in navigation and trigonometry?
Answer
(C)
An angle measured clockwise from North.
31
What are the most important items to remember when starting to solve the trigonometric ratios?
Answer
(D)
All of the above
32
If tan(θ) = Opposite/Adjacent, what is the cotangent (cot θ) of the same angle?
Answer
(C)
Adjacent/Opposite
33
In the formula a^2 = b^2 + c^2 - 2bc*cosA, which side is opposite to angle A?
Answer
(C)
Side a
34
What trigonometric function can be used if you know the opposite and hypotenuse sides?
Answer
(A)
Sine
35
Which of the following statements describes the relationship between sine and cosine functions for supplementary angles?
Answer
(C)
sin(180 - θ) = sin θ
36
Which formula is used to calculate the distance between two points in a coordinate plane (a, b) and (c, d)?
Answer
(C)
√((c-a)^2 + (d-b)^2)
37
What type of trigonometry is combined with Pythagoras' theorem in the cosine rule?
Answer
(B)
Right-angled trigonometry
38
When using the sine function, what sides of the right triangle are involved?
Answer
(B)
Opposite and Hypotenuse
39
Which of the following is a correct step to solve a right-angle triangle?
Answer
A
B
C
D
40
Which of the following statements about the cosine function is true?
Answer
(C)
Its range is from -1 to 1.
41
In triangle PQR, p = 5 cm, q = 7 cm, and angle R = 60°. What is the approximate length of side r?
Answer
(B)
6.5 cm
42
Which of the following is a correct statement concerning trigonometric functions and obtuse angles?
Answer
(C)
The sine function is positive in obtuse angles.
43
In a right triangle, the angle of elevation from point A to point B is the angle between the horizontal and which line?
Answer
(A)
The line from A to B
44
What type of angle is formed by the horizontal and the line of sight when looking upwards?
Answer
(B)
Angle of Elevation
45
Which of the following describes the term 'adjacent' when using trigonometry?
Answer
(C)
The side next to the angle, that isn't the hypotenuse.
46
In the context of the cosine rule, what do you need to know to use it?
Answer
A
B
47
To solve problems with the trigonometric ratios, what should your calculator be set to?
Answer
(B)
Degrees
48
Which trigonometric function is used to find an angle given the opposite and hypotenuse sides?
Answer
(A)
Sine
49
How can the Pythagorean theorem be used?
Answer
A
B
50
Which trigonometric ratio is defined as Opposite/Hypotenuse?
Answer
(A)
Sine