10 questions · Form 5 Mathematics Bab 6: Ratios and Graphs of Trigonometric Functions
What is the exact value of tan(315°)?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the exact value of tan(315°)?
Answer: B
315° is in Quadrant IV (tangent is negative). Reference angle = 360° - 315° = 45°. tan(315°) = -tan(45°) = -1.
2. If sin θ = 0.6 and θ is an obtuse angle (90° < θ < 180°), what is the value of cos θ?
Answer: A
In Quadrant II, cos θ is negative. Using sin²θ + cos²θ = 1 => cos θ = -√(1 - 0.6²) = -√(0.64) = -0.8.
3. In which quadrant are both sine and tangent negative, while cosine is positive?
Answer: A
By the ASTC rule, in Quadrant IV only cosine is positive; sine and tangent are negative.
4. Calculate the value of sin(150°) + cos(60°).
Answer: A
sin(150°) = sin(30°) = 12. cos(60°) = 12. Total = 12 + 12 = 1.
5. State the maximum and minimum values of the function y = 2 sin x - 1.
Answer: A
Maximum = 2(1) - 1 = 1. Minimum = 2(-1) - 1 = -3.
6. Which of the following points lies on the curve y = cos x?
Answer: A
cos(90°) = 0, so the point (90°, 0) lies on y = cos x.
7. At which of the following angles in 0° ≤ x ≤ 360° does y = cos x reach its minimum value?
Answer: C
cos(180°) = -1, which is the minimum value for the cosine function.
8. What is the period of the function y = sin(2x)?
Answer: C
Period for sine function = 360° / b = 360° / 2 = 180°.
9. What is the period of the tangent graph y = tan(3x)?
Answer: A
The period of tan(bx) is 180° / b = 180° / 3 = 60°.
10. If tan θ = 34 and θ is in Quadrant III, find the value of sin θ.
Answer: A
In Q III, opposite = -3, adjacent = -4, hypotenuse = √((-3)² + (-4)²) = 5. sin θ = opposite / hypotenuse = -35.