All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
1871
Find the value of cos(60°).
Answer:
1/2
In a right triangle, cos(60°) is equivalent to sin(30°) due to complementary angles. Since sin(30°) = 1/2, it strictly follows that cos(60°) is also exactly 1/2.
1872
What is the maximum value of the function y = sin(x)?
Answer:
1
The sine function represents the y-coordinate of a point on the unit circle. The maximum y-coordinate on a unit circle (radius 1) is exactly 1, occurring at 90°, 450°, etc. Therefore, the maximum value of sin(x) is 1.
1873
If sin(θ) = 4/5 and θ is in the first quadrant, what is cos(θ)?
Answer:
3/5
Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we get (4/5)² + cos²(θ) = 1. This gives 16/25 + cos²(θ) = 1, so cos²(θ) = 1 - 16/25 = 9/25. Since θ is in the first quadrant, cosine is positive, so cos(θ) = 3/5.
1874
Which of the following is equivalent to cot(θ)?
Answer:
1/tan(θ)
The cotangent function, cot(θ), is defined as the ratio of the adjacent side to the opposite side. This is the exact reciprocal of the tangent function (opposite/adjacent). Therefore, cot(θ) = 1 / tan(θ) or cos(θ)/sin(θ).
1875
Convert π/3 radians into degrees.
Answer:
60°
To convert radians to degrees, we multiply by (180 / π). Therefore, (π / 3) * (180 / π) = 180 / 3 = 60°.
1876
The shadow of a vertical tower is equal to its height. What is the angle of elevation of the sun?
Answer:
45°
Let the height of the tower be 'h' and the length of the shadow be 'x'. We are given h = x. The tangent of the angle of elevation θ is tan(θ) = opposite/adjacent = h/x. Since h = x, tan(θ) = 1. The angle whose tangent is 1 is 45°.
1877
If an observer looks up at the top of a tower, the angle formed by the line of sight and the horizontal is called the:
Answer:
Angle of elevation
When an observer looks at an object that is higher than their horizontal eye level, they must raise their eyes. The angle formed between the horizontal line and the upward line of sight is defined as the angle of elevation.
1878
What is the value of tan(90°)?
Answer:
Undefined
By definition, tan(θ) = sin(θ) / cos(θ). At 90 degrees, sin(90°) = 1 and cos(90°) = 0. Therefore, tan(90°) = 1 / 0, which involves division by zero and is mathematically undefined.
1879
Evaluate: sin(90° - θ)
Answer:
cos(θ)
In a right triangle, the two acute angles are complementary (sum to 90°). The sine of one acute angle (opposite/hypotenuse) is exactly the cosine (adjacent/hypotenuse) of the other acute angle. Thus, sin(90° - θ) = cos(θ).
1880
If tan(θ) = 1, what is the principal value of θ in degrees?
Answer:
45°
The tangent of an angle is 1 when the opposite side equals the adjacent side in a right-angled triangle. This forms an isosceles right triangle, meaning the two acute angles must both be exactly 45°.