Fundamentals of Trigonometry

Test your knowledge of Trigonometry with this quiz covering key concepts from Chapter 9 of first-year mathematics. The Fundamentals of Trigonometry MCQS Quiz includes questions on:

• Degree and radian conversions (e.g., $1^{\circ}$ to radians, $\frac{\pi}{4}$​ rad to degrees)
• Arc length and sector area calculations
• Complementary and coterminal angles
• Standard position and quadrantal angles
• Trigonometric identities (e.g., $sin^2\theta$+cos^2\theta$, $1+tan^2\theta$)

Perfect for intermediate students looking to strengthen their understanding of trigonometric fundamentals. Take the Fundamentals of Trigonometric MCQS Quiz now and check your mastery of angles, conversions, and identities!

Online Fundamentals of Trigonometry MCQs from Intermediate First Year Mathematics Chapter 9

1. The area of the sector of a circle of radius $r$ is

 $\frac{1}{2}r^2\theta$

 $\frac{1}{2}(r\theta)^2$

 $\frac{1}{2}r\theta^2$

 $\frac{1}{2r^2\theta}$

2. $\frac{\pi}{4}$ radian = ————- deg

 $60^{\circ}$

 $75^{\circ}$

 $30^{\circ}$

 $45^{\circ}$

3. If angle $\theta$ is in radian then angle counterminal with $\theta$ is

 $\theta + k\pi, k\in Z$

 $-\theta + 2k\pi, k\in Z$

 $\theta + 2k\pi, k\in Z$

 $-(\theta + 2\pi)$

4. If angle $\theta$ is in degrees, then the angle complementary to $\theta$ is

 None of these

 $\theta + 90^{\circ}k, k$

 $\theta + 180^{\circ}k, k\in Z$

 $\theta + 360^{\circ}k, k\in Z$

5. If the vertex lies at the origin of the rectangular coordinate system and its initial side is along the positive x-axis, then the angle is called

 Acute angle

 Coterminal angle

 Angle in standard position

 Quadrental angle

6. An angle is in standard position if its vertex lies

 At y-axis

 At x-axis

 At origin

 in 1st Quadrant

7. If $\theta=45^{\circ}$, $r=18$mm then $l=?$

 $\frac{9}{2}\pi$

 810mm

 $\frac{2}{9}\pi$

 810

8. $105^{\circ}$ = ———- radian

 $\frac{5\pi}{12}$

 $\frac{2\pi}{3}$

 $\frac{5\pi}{6}$

 $\frac{7\pi}{12}$

9. $sin^2\theta + cos^2\theta$ is equal to

 -1

 0

 1

 $Sec^2 \theta$

10. 1 Radian is equal to

 $\frac{\pi}{180}$ rad

 $\left(\frac{\pi}{180}\right)^{\circ}$

 $\left(\frac{180}{\pi}\right)^{\circ}$

 $\frac{180}{\pi}$ rad

11. If $l=1.5$cm and $r=2.5c$ then $\theta$ is equal to

 None of these

 3.75

 $\frac{3}{5}$

 $\frac{5}{3}$

12. $1+tan^2\theta$ is equal to

 $Sin^2\theta$

 $Cosec^2 \theta$

 $Cot^2\theta$

 $Sec^2\theta$

13. Angles with the same initial and terminal sides are called

 Allied angles

 Quad rental angle

 Acute angles

 Coterminal angles

14. The circular measure of the angle between the hands of a watch at 4 o’clock is

 $270^{\circ}$

 $120^{\circ}$

 $45^{\circ}$

 $\frac{3\pi}{2}$

15. 3” = ——— radian

 $\frac{\pi}{216000}$

 $\frac{27721\pi}{32400}$

 $\frac{41\pi}{720}$

 $\frac{53\pi}{270}$

16. If the initial and the terminal side of an angle falls on the x-axis or y-axis, then it is called

 Quadrantal angle

 Coterminal angle

 Allied angles

 None of these

17. $0^{\circ}, 90^{\circ}, 180^{\circ}, 270^{\circ}$ and $360^{\circ}$ are

 Allied angles

 None of these

 Quadrantal angle

 Coterminal angle

18. 1 radian is equal to

 $17.5270^{\circ}$

 $57.296^{\circ}$

 $17527^{\circ}$

 $5.7296^{\circ}$

19. $1^{\circ}$ is equal to

 1.75 rad

 0.00175 rad

 0.0175 rad

 0.175 rad

20. 3 radian is equal to

 $270^{\circ}$

 $171.888^{\circ}$

 $120^{\circ}$

 $300^{\circ}$

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Online Fundamentals of Trigonometry MCQs with Answers

• $1^{\circ}$ is equal to
• 1 Radian is equal to
• 1 radian is equal to
• 3 radian is equal to
• $105^{\circ}$ = ———- radian
• 3” = ——— radian
• $\frac{\pi}{4}$ radian = ————- deg
• The circular measure of the angle between the hands of a watch at 4 o’clock is
• If $l=1.5$cm and $r=2.5c$ then $\theta$ is equal to
• If $\theta=45^{\circ}$, $r=18$mm then $l=?$
• The area of the sector of a circle of radius $r$ is
• Angles with the same initial and terminal sides are called
• If angle $\theta$ is in degrees, then the angle complementary to $\theta$ is
• If angle $\theta$ is in radian then angle coterminal with $\theta$ is
• If the vertex lies at the origin of the rectangular coordinate system and its initial side is along the positive x-axis, then the angle is called
• An angle is in standard position if its vertex lies
• If the initial and the terminal side of an angle falls on the x-axis or y-axis, then it is called
• $0^{\circ}, 90^{\circ}, 180^{\circ}, 270^{\circ}$ and $360^{\circ}$ are
• $sin^2\theta + cos^2\theta$ is equal to
• $1+tan^2\theta$ is equal to

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