Trigonometry Advanced Trigonometric Concepts 2 ā Questions and Answers
Question 1: What is the value of sin(75Ā°) using the sum formula?
- (ā6 + ā2) / 4 (Correct answer)
- (ā6 - ā2) / 4
- (ā3 + 1) / 4
- (ā3 - 1) / 2
Correct answer: (ā6 + ā2) / 4
sin(75Ā°) = sin(45Ā° + 30Ā°) = sin45Ā·cos30 + cos45Ā·sin30 = (ā2/2)(ā3/2) + (ā2/2)(1/2) = (ā6 + ā2)/4.
Question 2: Which identity correctly expresses cos(2Īø) in terms of sin(Īø) only?
- 1 - 2sinĀ²Īø (Correct answer)
- 2sinĀ²Īø - 1
- 1 + 2sinĀ²Īø
- sinĀ²Īø - cosĀ²Īø
Correct answer: 1 - 2sinĀ²Īø
cos(2Īø) = cosĀ²Īø - sinĀ²Īø = (1 - sinĀ²Īø) - sinĀ²Īø = 1 - 2sinĀ²Īø.
Question 3: What is the period of y = 3sin(4x - Ļ)?
- Ļ/2 (Correct answer)
- 2Ļ
- 4Ļ
- Ļ
Correct answer: Ļ/2
The period of y = AĀ·sin(Bx + C) is 2Ļ/|B|, so 2Ļ/4 = Ļ/2.
Question 4: The expression tan(Ī± - Ī²) equals which of the following?
- (tanĪ± - tanĪ²) / (1 + tanĪ± tanĪ²) (Correct answer)
- (tanĪ± + tanĪ²) / (1 - tanĪ± tanĪ²)
- (tanĪ± - tanĪ²) / (1 - tanĪ± tanĪ²)
- tanĪ± - tanĪ²
Correct answer: (tanĪ± - tanĪ²) / (1 + tanĪ± tanĪ²)
The tangent subtraction formula is tan(Ī± - Ī²) = (tanĪ± - tanĪ²) / (1 + tanĪ± tanĪ²).
Question 5: If sec Īø = 2 and Īø is in the first quadrant, what is tan Īø?
- ā3 (Correct answer)
- 1/ā3
- 2
- ā2
Correct answer: ā3
sec Īø = 2 means cos Īø = 1/2, so Īø = 60Ā°, and tan 60Ā° = ā3.
Question 6: Which of the following is equivalent to 2 sin Īø cos Īø?
- sin(2Īø) (Correct answer)
- cos(2Īø)
- tan(2Īø)
- sinĀ²Īø - cosĀ²Īø
Correct answer: sin(2Īø)
The double-angle identity states sin(2Īø) = 2 sinĪø cosĪø.
Question 7: What is the range of the function y = arcsin(x)?
- [-Ļ/2, Ļ/2] (Correct answer)
- [0, Ļ]
- (-Ļ, Ļ)
- [-1, 1]
Correct answer: [-Ļ/2, Ļ/2]
The range of arcsin(x) is restricted to [-Ļ/2, Ļ/2] to make it a function.
Trigonometry Advanced Trigonometric Concepts 2
What is the value of sin(75Ā°) using the sum formula?