Period of tan(5x/7) is:
- 5π/7
- 5π
- 7π/5
- 7π
Show answer and explanation
Answer: C. 7π/5
Period of tan(kx)=π/k; k=5/7 ⇒ π/(5/7)=7π/5.
FSC Mathematics: Fundamentals of Trigonometry, questions with answers
Practise 26 real Federal Board questions on Fundamentals of Trigonometry from 2023 to 2026. See the answer and explanation as soon as you answer.
26real questions
13multiple choice
5exam sessions
About Fundamentals of Trigonometry in FSC Mathematics
Fundamentals of Trigonometry is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th and 12th class), and about 5% of its real questions come from it. Tayyari Karo has 26 real questions on this chapter from 2023 to 2026; 13 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 16 easy, 8 medium, 2 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
Range of a+bsin2θ is:
- a±b
- a+b
- a−b
- 2(a±b)
Show answer and explanation
Answer: A. a±b
sin2θ∈[−1,1] ⇒ range is [a−b, a+b].
The number of solutions of cosx=0.3 in [0,2π) is:
- 0
- 1
- 2
- 4
Show answer and explanation
Answer: C. 2
cosx=0.3 has exactly two solutions in one full period.
If tanθ=2, what is the value of Cosθ when θ is in the first quadrant?
- 1/√3
- 2/√5
- √5
- 1/√5
Show answer and explanation
Answer: D. 1/√5
tanθ=2 ⇒ opp=2,adj=1,hyp=√5 ⇒ cosθ=1/√5.
The maximum value of 3+4sinθ is:
- 3
- 4
- 7
- −1
Show answer and explanation
Answer: C. 7
sinθ max=1 ⇒ 3+4(1)=7.
What is the period of 3Sin(x/5)?
- 10π
- 30π
- π/5
- 5π
Show answer and explanation
Answer: A. 10π
Period of Sin(kx) is 2π/k. Here k = 1/5, so period = 2π/(1/5) = 10π (the factor 3 does not affect the period).
Find the maximum and minimum values of: y=1/(4+5cos3x)
Show model answer
cos3x∈[−1,1] ⇒ denominator D=4+5cos3x∈[−1,9]
At D=9 (cos3x=1): y=1/9 (smallest positive value)
At D=−1 (cos3x=−1): y=−1 (largest negative value)
y=−1 and y=1/9 are the extreme values reached at the endpoints of the denominator's range (note y is unbounded near D=0, where cos3x=−4/5)
Find the maximum and minimum values of the function f(θ) = 1/(3+5cos(2θ+π))
Show model answer
3+5cos(2θ+π) = 3−5cos2θ; since cos2θ∈[−1,1], denominator D∈[−2,8]
Largest positive D=8 (cos2θ=−1) gives smallest positive f: f=1/8
Most negative D=−2 (cos2θ=1) gives f=−1/2
Maximum value ≈ −1/2 (at D=−2), minimum positive branch value = 1/8 (at D=8) — note f is unbounded near D=0.
Sessions with Fundamentals of Trigonometry questions
| Session | Questions |
|---|---|
| 2026 Annual | 12 |
| 2025 1st Annual | 6 |
| 2025 2nd Annual | 4 |
| 2024 Annual | 2 |
| 2023 Annual | 2 |
Common questions
What does the Fundamentals of Trigonometry chapter cover on this page?
26 real Federal Board (FBISE) Mathematics questions on Fundamentals of Trigonometry from 2023 to 2026, for 11th and 12th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
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