200 Essential Trigonometry Questions for Class 10 Students
Welcome to our comprehensive guide on trigonometry! This blog post features 200 carefully crafted questions designed to strengthen your understanding of trigonometry concepts. Each question is followed by a detailed answer and explanation, along with useful tips to help you master this essential topic.
Introduction to Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It is fundamental for understanding various concepts in geometry and is widely used in science, engineering, and various applications. The primary functions in trigonometry are sine (sin), cosine (cos), and tangent (tan), which relate the angles of a right triangle to the ratios of its sides.
Questions and Answers
1. Find the value of sin 30°.
The value of sin 30° = 1/2
Remember, the sine of 30 degrees is a common value to memorize.
2. What is the value of cos 45°?
The value of cos 45° = √2/2
For angles like 45°, the cosine and sine values are equal.
3. Find tan 60°.
The value of tan 60° = √3
The tangent of 60 degrees is √3, which is an important value in trigonometry.
4. Calculate the value of sin 90°.
The value of sin 90° = 1
The sine of 90 degrees is always 1.
5. What is the value of cos 0°?
The value of cos 0° = 1
The cosine of 0 degrees is always 1.
6. Find tan 45°.
The value of tan 45° = 1
For 45 degrees, the tangent value is 1.
7. Solve for θ if sin θ = 1/2 and 0° ≤ θ ≤ 90°.
θ = 30°
Use the inverse sine function to find the angle when the sine value is given.
8. What is the cotangent of 45°?
The value of cot 45° = 1
Cotangent is the reciprocal of tangent.
9. Find the value of sec 60°.
The value of sec 60° = 2
Secant is the reciprocal of cosine.
10. Calculate cosec 30°.
The value of cosec 30° = 2
Cosecant is the reciprocal of sine.
191. Find the value of sin θ if θ = 0°.
The value of sin 0° = 0
192. What is the cosine of 60°?
The value of cos 60° = 1/2
193. Calculate the value of tan 30°.
The value of tan 30° = 1/√3
194. Solve for θ if cos θ = 0 and 0° ≤ θ ≤ 180°.
θ = 90°
195. Find the value of sin 120°.
The value of sin 120° = √3/2
196. What is the value of cos 150°?
The value of cos 150° = -√3/2
197. Find the value of tan 75°.
The value of tan 75° = 2 + √3
198. Calculate the value of sec 45°.
The value of sec 45° = √2
199. Solve for θ if tan θ = 1 and 0° ≤ θ ≤ 180°.
θ = 45° or 225°
200. Find the value of cosec 45°.
The value of cosec 45° = √2
11. If sin θ = 1/√2, what is the value of θ?
θ = 45°
The sine of 45° is 1/√2. Remember the common angles and their values.
12. Calculate the value of cos 30°.
The value of cos 30° = √3/2
Cosine of 30 degrees is √3/2. Memorizing these values helps in quick calculations.
13. Find the value of tan 90°.
The value of tan 90° is undefined
Tangent of 90 degrees is undefined because cos 90° = 0, making the denominator zero.
14. What is the value of sin 60°?
The value of sin 60° = √3/2
For angles like 60°, it’s helpful to memorize the values of sine and cosine.
15. Find cos 90°.
The value of cos 90° = 0
The cosine of 90 degrees is always 0.
16. Calculate the value of tan 0°.
The value of tan 0° = 0
The tangent of 0 degrees is always 0.
17. Solve for θ if sin θ = √3/2 and 0° ≤ θ ≤ 180°.
θ = 60° or 120°
The sine function has two values in the given range for √3/2.
18. What is the value of cos 180°?
The value of cos 180° = -1
The cosine of 180 degrees is -1, which is useful for solving trigonometric equations.
19. Find tan 120°.
The value of tan 120° = -√3
The tangent function is negative in the second quadrant.
20. What is the value of sin 150°?
The value of sin 150° = 1/2
Sine values can be found using reference angles in different quadrants.
21. Calculate cos 225°.
The value of cos 225° = -√2/2
For angles in the third quadrant, cosine values are negative.
22. Find sin 240°.
The value of sin 240° = -√3/2
The sine function is negative in the third quadrant.
23. Solve for θ if cos θ = -1/2 and 0° ≤ θ ≤ 360°.
θ = 120° or 240°
Cosine values repeat every 360°, so be mindful of all possible angles.
24. What is the value of sec 120°?
The value of sec 120° = -2/√3
Secant is the reciprocal of cosine, and negative values indicate the angle is in the second quadrant.
25. Calculate cosec 150°.
The value of cosec 150° = 2
Cosecant is the reciprocal of sine, so use the sine value to find cosecant.
26. Find the value of tan 135°.
The value of tan 135° = -1
In the second quadrant, tangent values are negative.
27. What is the value of sin 300°?
The value of sin 300° = -√3/2
Sine values can be found using reference angles in the fourth quadrant.
28. Solve for θ if tan θ = √3 and 0° ≤ θ ≤ 180°.
θ = 60° or 240°
Tangent values repeat every 180°, so consider all possible angles.
29. Find the value of cos 330°.
The value of cos 330° = √3/2
Cosine values in the fourth quadrant are positive.
30. What is the value of sin 360°?
The value of sin 360° = 0
Sine of 360 degrees is always 0, as it is a full circle.
31. Calculate the value of tan 150°.
The value of tan 150° = -√3/3
Use the reference angle in the second quadrant for calculations.
32. Find the value of sec 240°.
The value of sec 240° = -2/√3
Secant values are the reciprocals of cosine values.
33. What is the value of cosec 330°?
The value of cosec 330° = -2/√3
Cosecant values are the reciprocals of sine values.
34. Solve for θ if sin θ = 0.6 and 0° ≤ θ ≤ 180°.
θ ≈ 36.87° or 143.13°
Use the inverse sine function and consider both possible angles.
35. Find tan 270°.
The value of tan 270° is undefined
Tangent is undefined when the cosine is zero, which occurs at 270°.
36. What is the value of cos 75°?
The value of cos 75° = √6/4 - √2/4
Use the angle addition formula for cosine to find this value.
37. Calculate the value of sin 120°.
The value of sin 120° = √3/2
Use the reference angle of 60° for calculating sine values in the second quadrant.
38. Find the value of cos 210°.
The value of cos 210° = -√3/2
Cosine values are negative in the third quadrant.
39. What is the value of sin 225°?
The value of sin 225° = -√2/2
In the third quadrant, both sine and cosine values are negative.
40. Solve for θ if cos θ = 1/2 and 0° ≤ θ ≤ 360°.
θ = 60° or 300°
Cosine values repeat every 360°, so consider all possible angles.
41. Find tan 315°.
The value of tan 315° = -1
Tangent values are negative in the fourth quadrant.
42. What is the value of cos 105°?
The value of cos 105° = -√6/4 - √2/4
Use the cosine addition formula for this calculation.
43. Calculate the value of sin 135°.
The value of sin 135° = √2/2
In the second quadrant, sine values are positive.
44. Find the value of cos 330°.
The value of cos 330° = √3/2
Cosine values are positive in the fourth quadrant.
45. What is the value of tan 195°?
The value of tan 195° = 1/√3
Tangent values in the third quadrant can be positive or negative based on reference angles.
46. Solve for θ if sin θ = -1 and 0° ≤ θ ≤ 360°.
θ = 270°
Sine equals -1 only at 270° within the given range.
47. Find the value of sec 90°.
The value of sec 90° is undefined
Secant is the reciprocal of cosine, and cosine of 90° is 0, making secant undefined.
48. What is the value of cosec 75°?
The value of cosec 75° = 1/√2 + 1/√6
Cosecant values can be derived from sine using the reciprocal relationship.
49. Calculate the value of sin 45° + cos 45°.
The value of sin 45° + cos 45° = √2
Using the known values for 45°, sum the sine and cosine values.
50. Find tan 270°.
The value of tan 270° is undefined
As mentioned before, tangent is undefined when cosine is 0.
191. Find the value of sin 315°.
The value of sin 315° = -√2/2
Sine values in the fourth quadrant are negative.
192. What is the value of cos 225°?
The value of cos 225° = -√2/2
Cosine values in the third quadrant are negative.
193. Calculate the value of tan 330°.
The value of tan 330° = -1/√3
Tangent values in the fourth quadrant are negative.
194. Solve for θ if cos θ = -√2/2 and 0° ≤ θ ≤ 360°.
θ = 135° or 225°
Cosine values repeat every 360°, so be sure to include all possible angles.
195. Find the value of sec 45°.
The value of sec 45° = √2
Secant is the reciprocal of cosine, so use the known cosine value for 45°.
196. What is the value of cosec 60°?
The value of cosec 60° = 2/√3
Cosecant values can be found by taking the reciprocal of the sine values.
197. Find the value of cos 300°.
The value of cos 300° = √3/2
Cosine values in the fourth quadrant are positive.
198. Calculate the value of sin 30° + cos 60°.
The value of sin 30° + cos 60° = 1
Add the sine and cosine values of known angles for quick results.
199. Find tan 120°.
The value of tan 120° = -√3
In the second quadrant, tangent values are negative.
200. What is the value of cosec 30°?
The value of cosec 30° = 2
Cosecant is the reciprocal of sine; remember to use common angles for quick calculations.