Trigonometry Core Concepts 3 — Questions and Answers
Question 1: What does the Pythagorean identity state?
- sin²θ + cos²θ = 1 (Correct answer)
- sinθ + cosθ = 1
- tan²θ + 1 = sec θ
- sin²θ - cos²θ = 1
Correct answer: sin²θ + cos²θ = 1
The fundamental Pythagorean identity sin²θ + cos²θ = 1 follows directly from the unit circle definition.
Question 2: What is the range of the sine function?
- [-1, 1] (Correct answer)
- [0, 1]
- (-∞, ∞)
- [0, ∞)
Correct answer: [-1, 1]
The sine function oscillates between -1 and 1 inclusive for all real inputs.
Question 3: If cos(θ) = 3/5, what is sin(θ) for θ in Quadrant I?
- 4/5 (Correct answer)
- 3/4
- 5/3
- 1/5
Correct answer: 4/5
Using sin²θ + cos²θ = 1: sin²θ = 1 - 9/25 = 16/25, so sin(θ) = 4/5 in Q I.
Question 4: What is the amplitude of y = 3sin(x)?
- 3 (Correct answer)
- 1
- π
- 6
Correct answer: 3
The amplitude is the absolute value of the coefficient in front of the trig function, which is 3.
Question 5: Which angle has a tangent value that is undefined?
- 90° (Correct answer)
- 45°
- 0°
- 180°
Correct answer: 90°
At 90°, cos(90°) = 0, making tan(90°) = sin/cos = 1/0, which is undefined.
Question 6: What is the reference angle for 225°?
- 45° (Correct answer)
- 135°
- 225°
- 315°
Correct answer: 45°
225° is in Quadrant III; its reference angle is 225° - 180° = 45°.
Question 7: What is cot(θ) expressed in terms of sin and cos?
- cos(θ)/sin(θ) (Correct answer)
- sin(θ)/cos(θ)
- 1/cos(θ)
- 1/sin(θ)
Correct answer: cos(θ)/sin(θ)
Cotangent is the reciprocal of tangent, so cot(θ) = cos(θ)/sin(θ).
Trigonometry Core Concepts 3
What does the Pythagorean identity state?