PRE CALCULUS Trigonometry — Questions and Answers
Question 1: What is sin(30°)?
- 0
- 1/2 (Correct answer)
- √2/2
- √3/2
Correct answer: 1/2
sin(30°) = 1/2 is one of the fundamental trigonometric values that should be memorized, derived from the 30-60-90 special right triangle.
Question 2: What is the unit circle?
- A circle with diameter 1
- A circle with radius 1 centered at the origin, used to define trigonometric functions for all angles (Correct answer)
- Any circle used in calculations
- A circle in unit conversion
Correct answer: A circle with radius 1 centered at the origin, used to define trigonometric functions for all angles
The unit circle has radius 1 and center at (0,0). Any point on it has coordinates (cos θ, sin θ), defining trig functions for all angles.
Question 3: What is the period of the standard sine function y = sin(x)?
- π
- 2π (Correct answer)
- π/2
- 4π
Correct answer: 2π
The sine function completes one full cycle every 2π radians (360°), returning to its starting value after this interval.
Question 4: What is the Pythagorean identity?
- a² + b² = c²
- sin²θ + cos²θ = 1 (Correct answer)
- tan θ = sin θ / cos θ
- sin θ = cos(90° - θ)
Correct answer: sin²θ + cos²θ = 1
sin²θ + cos²θ = 1 is the fundamental Pythagorean identity, derived from the Pythagorean theorem applied to the unit circle.
Question 5: What is the tangent of an angle in terms of sine and cosine?
- tan θ = cos θ / sin θ
- tan θ = sin θ / cos θ (Correct answer)
- tan θ = sin θ × cos θ
- tan θ = sin θ + cos θ
Correct answer: tan θ = sin θ / cos θ
Tangent is defined as the ratio of sine to cosine: tan θ = sin θ / cos θ. This is undefined when cos θ = 0.
Question 6: In which quadrant are both sine and cosine positive?
- Quadrant I (Correct answer)
- Quadrant II
- Quadrant III
- Quadrant IV
Correct answer: Quadrant I
In Quadrant I (0° to 90°), both x and y coordinates are positive on the unit circle, making both cosine (x) and sine (y) positive.
PRE CALCULUS Trigonometry
What is sin(30°)?