Trigonometry, the study of relationships involving lengths and angles of triangles, has always been a fascinating subject for students. From understanding the basics of sine, cosine, and tangent to exploring the depths of their properties, trigonometry finds its application in various fields like physics, engineering, astronomy, and even music. To test your understanding of trigonometric functions, we’ve compiled a list of 20 simple multiple-choice questions. Let’s dive right in!
1. The value of sin(90° – θ) is:
Answer:
Explanation:
The function sin(90° – θ) is equivalent to cosθ.
2. The period of the function tanθ is:
Answer:
Explanation:
The function tanθ repeats its values after an interval of 180°.
3. The value of cos(360° + θ) is:
Answer:
Explanation:
Cosine function has a periodicity of 360°.
4. The principal value of sin^(-1)(-1/2) is:
Answer:
Explanation:
The angle whose sine value is -1/2 in the principal range is -30°.
5. If cosθ = 3/5 and θ is acute, then sinθ is:
Answer:
Explanation:
Using the Pythagorean identity, sin²θ + cos²θ = 1, we can find sinθ = 4/5.
6. The domain of secθ is:
Answer:
Explanation:
Secθ is not defined for values where cosθ = 0.
7. The maximum value of sinθ is:
Answer:
Explanation:
The sine function ranges between -1 and 1.
8. Which of the following is not a trigonometric identity?
Answer:
Explanation:
The correct identity is secθ = 1/cosθ.
9. If sinA = 3/5 and A is acute, then cosA is:
Answer:
Explanation:
Using the Pythagorean identity, we can find cosA = 4/5.
10. The value of cos(-θ) is:
Answer:
Explanation:
The cosine function is even, hence cos(-θ) = cosθ.
11. The range of sinθ is:
Answer:
Explanation:
The sine function gives values between -1 and 1, inclusive.
12. The angle of elevation of the sun when the shadow of a pole is √3 times its height is:
Answer:
Explanation:
Let the height of the pole be h. The shadow length is √3h. Using tanθ = h/(√3h), we get θ = 30°.
13. The general solution of sinθ = 0 is:
Answer:
Explanation:
The sine function is zero at integral multiples of π.
14. If tan(α + β) = 1 and tan(α – β) = 1/3, then the value of tanα is:
Answer:
Explanation:
Using the formulae for tan(α + β) and tan(α – β), and solving the equations, we get tanα = 2/3.
15. The value of 2cos²θ – 1 is equivalent to:
Answer:
Explanation:
The given expression is the double angle formula for cosine.
16. If cscθ = 2, then the value of sinθ is:
Answer:
Explanation:
cscθ is the reciprocal of sinθ. Hence, sinθ = 1/2.
17. The period of cosθ is:
Answer:
Explanation:
The cosine function completes one full cycle over an interval of 360°.
18. The value of tan(45° + θ) in terms of tanθ is:
Answer:
Explanation:
Using the tan addition formula.
19. If sinθ = 4/5 and θ lies in the second quadrant, the value of cosθ is:
Answer:
Explanation:
In the second quadrant, cosine is negative and using the Pythagorean identity, we get cosθ = -3/5.
20. The principal value of cos^(-1)(-√3/2) is:
Answer:
Explanation:
The angle in the principal range for which cosine is -√3/2 is 150°.