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
1831
If tan(A) = cot(B), which of the following is true for acute angles A and B?
Answer:
A + B = 90°
The tangent of an angle is equal to the cotangent of its complement. Therefore, if tan(A) = cot(B), it implies that angles A and B must be complementary, meaning their sum A + B must equal 90°.
1832
What is the period of the function y = tan(x)?
Answer:
π
Unlike the sine and cosine functions which have a period of 2π, the tangent function repeats its complete cycle over an interval of π radians (or 180 degrees).
1833
Evaluate: sin²(20°) + sin²(70°)
Answer:
1
Since 20° and 70° are complementary, sin(70°) = cos(20°). Therefore, sin²(70°) = cos²(20°). Substituting this into the expression gives sin²(20°) + cos²(20°), which by the Pythagorean identity always equals 1.
1834
According to the Sine Rule for a triangle with sides a,b,c and opposite angles A,B,C, what is a/sin(A) equal to?
Answer:
b/sin(B)
The Law of Sines establishes that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides of a given triangle. Thus, a/sin(A) = b/sin(B) = c/sin(C).
1835
Which of the following relates the sides of any triangle to the cosines of its angles?
Answer:
Cosine Rule
The Cosine Rule (Law of Cosines) relates the lengths of the sides of a triangle to the cosine of one of its angles, typically expressed as c² = a² + b² - 2ab*cos(C).
1836
Evaluate: sec(60°)
Answer:
2
The secant function is the reciprocal of the cosine function. We know that cos(60°) = 1/2. Therefore, taking the reciprocal gives sec(60°) = 2/1 = 2.
1837
If the angle of elevation of the sun is 45°, what is the length of the shadow of a 10m tall tree?
Answer:
10 m
Let the shadow length be x. Using the tangent function: tan(45°) = height / shadow = 10 / x. Since tan(45°) = 1, we have 1 = 10 / x, which means x = 10 meters.
1838
Simplify the expression: √(1 - cos²θ), where θ is an acute angle.
Answer:
sin(θ)
From the Pythagorean identity sin²θ + cos²θ = 1, we can derive sin²θ = 1 - cos²θ. Taking the square root of both sides gives √(1 - cos²θ) = |sin(θ)|. Since θ is an acute angle, sin(θ) is positive, so the result is simply sin(θ).
1839
Which of the following equals (sec²θ - 1)?
Answer:
tan²θ
Using the standard Pythagorean identity 1 + tan²θ = sec²θ, we can isolate the tangent term by subtracting 1 from both sides. This gives tan²θ = sec²θ - 1.
1840
Find the value of arcsin(1/2) in degrees.
Answer:
30°
The expression arcsin(1/2) asks for the angle within the principal range [-90°, 90°] whose sine is exactly 1/2. We know from standard triangles that sin(30°) = 1/2, so the answer is 30°.