Trigonometry Core Concepts 2 — Questions and Answers
Question 1: What is the reciprocal of the sine function?
- Cosecant (Correct answer)
- Secant
- Cotangent
- Cosine
Correct answer: Cosecant
Cosecant (csc) is defined as 1/sin(θ), making it the reciprocal of sine.
Question 2: In a right triangle, if the opposite side is 5 and the hypotenuse is 13, what is sin(θ)?
- 5/13 (Correct answer)
- 12/13
- 5/12
- 13/5
Correct answer: 5/13
Sine equals opposite over hypotenuse, so sin(θ) = 5/13.
Question 3: What is the period of the function f(x) = cos(x)?
- 2π (Correct answer)
- π
- π/2
- 4π
Correct answer: 2π
The cosine function completes one full cycle every 2π radians.
Question 4: Which quadrant contains an angle where sin > 0 and cos < 0?
- Quadrant II (Correct answer)
- Quadrant I
- Quadrant III
- Quadrant IV
Correct answer: Quadrant II
In Quadrant II, the y-coordinate (sine) is positive and the x-coordinate (cosine) is negative.
Question 5: What is tan(45°)?
- 1 (Correct answer)
- √2
- √3/2
- 0
Correct answer: 1
At 45°, sine and cosine are equal (both √2/2), so their ratio is 1.
Question 6: How many radians are in 180 degrees?
- π (Correct answer)
- 2π
- π/2
- π/4
Correct answer: π
By definition, 180° = π radians, which is the foundational radian conversion.
Question 7: What is the value of cos(0°)?
- 1 (Correct answer)
- 0
- -1
- √2/2
Correct answer: 1
At 0°, the point on the unit circle is (1, 0), so cosine equals 1.
Trigonometry Core Concepts 2
What is the reciprocal of the sine function?