1. The point P(−3, 4) is on the terminal side of an angle θ in standard position. Then cos θ is
- A−4/3
- B4/5
- C−3/5
- D3/5
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Answer: C. r = √(9 + 16) = 5 and cos θ = x/r = −3/5. 4/5 is sin θ and −4/3 is tan θ.
FSc Part 1 Maths chapter 9: Fundamentals of trigonometry MCQs with answers
By Team Megalecture · Updated 4 Nov 2026
20 exam-style questions on Fundamentals of trigonometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.
20 questions · 2 topics · 10 per test
What chapter 9 covers
- Angles and their measurement 10 questions
- Trigonometric ratios and fundamental identities 10 questions
Ten Fundamentals of trigonometry questions with answers
Try each one, then open the answer. These ten stay the same; the test draws new ones every time.
2. 1 + tan2θ is equal to
- Acot2θ
- Bcosec2θ
- Ccos2θ
- Dsec2θ
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Answer: D. Divide sin2θ + cos2θ = 1 by cos2θ: tan2θ + 1 = sec2θ. 1 + cot2θ = cosec2θ.
3. The expression (sec θ − tan θ)(sec θ + tan θ) is equal to
- A0
- B1
- C2 sec θ
- Dsec2θ + tan2θ
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Answer: B. It is a difference of squares: sec2θ − tan2θ = 1, from 1 + tan2θ = sec2θ.
4. An angle of 60° in radian measure is
- Aπ/4
- Bπ/6
- C2π/3
- Dπ/3
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Answer: D. Multiply degrees by π/180: 60 × π/180 = π/3.
5. If sin θ < 0 and tan θ > 0, the terminal side of θ lies in the
- Afirst quadrant
- Bsecond quadrant
- Cfourth quadrant
- Dthird quadrant
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Answer: D. sin is negative in quadrants III and IV; tan is positive in I and III. Both conditions hold only in quadrant III.
6. The value of cos 180° + sin 270° is
- A0
- B−2
- C2
- D−1
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Answer: B. At 180° the point on the unit circle is (−1, 0), so cos 180° = −1; at 270° it is (0, −1), so sin 270° = −1. Sum = −2.
7. If tan θ = −5/12 and the terminal side of θ is in the second quadrant, then cos θ is
- A5/13
- B12/13
- C−5/13
- D−12/13
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Answer: D. Take x = −12, y = 5 (quadrant II); r = 13. cos θ = x/r = −12/13. 5/13 is sin θ.
8. The value of sin245° + tan230° is
- A2/3
- B1
- C7/6
- D5/6
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Answer: D. sin 45° = 1/√2 so sin245° = 1/2; tan 30° = 1/√3 so tan230° = 1/3. Sum = 5/6.
9. An arc of length 11 cm lies on a circle of radius 3.5 cm. The angle it subtends at the centre is approximately
- A6.28 rad (about 360°)
- B0.32 rad (about 18°)
- C38.5 rad
- D3.14 rad (about 180°)
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Answer: D. θ = l/r = 11/3.5 ≈ 3.14 rad, which is π radians or about 180°. 0.32 comes from r/l, and 38.5 from multiplying.
10. The area of a sector of a circle of radius 6 cm with central angle π/3 is
- A12π cm2
- B6π cm2
- C2π cm2
- D36π cm2
Show answer
Answer: B. Area = ½r2θ = ½ × 36 × π/3 = 6π cm2. Forgetting the ½ gives 12π; 2π cm is the arc length.
Read the notes for this chapter
Ways to practise this chapter
- Chapter test. Ten questions from Fundamentals of trigonometry, drawn fresh each time, about ten minutes.
- Practice mode. The right answer and the explanation after every question, with no clock. Exam mode keeps the marks until the end and runs a timer.
- Hints. One tap for a nudge, a second to remove two wrong options.
- My mistakes. Every question you get wrong is kept, and leaves the list once you get it right.
- Formula sheet. All FSc Part 1 Maths rules on one page.
Fundamentals of trigonometry: questions students ask
How many Fundamentals of trigonometry MCQs are there?
20, each with the answer and a short explanation, across 2 topics: Angles and their measurement, Trigonometric ratios and fundamental identities. Every chapter test draws ten of them, so you can take it many times.
Is the FSc Part 1 Maths chapter 9 test free?
Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.
How is the chapter test marked?
The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.
Can I read the explanations in Urdu?
Yes. In practice mode and on your results you can switch the explanations to Urdu.
Keep going
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