CBSE Class 10 > Class 10 Notes > Mathematics (Maths) > Practice Questions: Introduction to Trigonometry
Practice Questions: Introduction to Trigonometry
Q1. If sec θ + tan θ = 7, then evaluate sec θ - tan θ.
Q2. Prove that
(1+tan A - sec A) (1+tan A + sec A) = 2 tan A
Q3. If tan A = cot B, then find the value of (A+B)
Q4. If sinθ + sin2θ = 1 then prove that cos2θ + cos4θ = 1.
Q5. If tan θ + cot θ = 5, find the value of tan2θ + cotθ.
Q6. If sec 2A = cosec (A - 27°) where 2A is an acute angle, find the measure of ∠A.
Q7. Evaluate: sin2 19° + sin271°.
Q8. In a triangle ABC, write cos(B+C/2) in terms of angle A.
Q9. If secθ sinθ = 0, then find the value of θ.
Q10. Find the value of sin241° + sin249°
Q11. If tan A = cot B, prove that A + B = 90°.
Q12. Express sin 67° + cos 75° in terms of ratios of angles between 0° and 45°.
Sol:
Q13. What is the value of sinθ. cos(90° - θ) + cosθ . sin(90° - θ)?
Q14. If tan θ = cot (30° + θ ), find the value of θ .
Q15. If sin 3θ = cos (θ - 6)° and 3θ and (θ - 6)° are acute angles, find the value of θ.
Q16. Show that: tan 10° tan 15° tan 75° tan 80° = 1
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FAQs on Practice Questions: Introduction to Trigonometry
| 1. What is the definition of trigonometry and its importance in mathematics? |  |
Ans.Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is important because it provides tools to solve problems involving angles and distances in various fields such as physics, engineering, computer graphics, and architecture.
| 2. What are the primary trigonometric functions, and how are they defined in relation to a right triangle? | |
Ans.The primary trigonometric functions are sine, cosine, and tangent. In a right triangle, these functions are defined as follows: - Sine (sin) of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. - Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. - Tangent (tan) of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
| 3. How do the unit circle and the right triangle relate to trigonometric functions? | |
Ans.The unit circle is a circle with a radius of one, centered at the origin of a coordinate plane. It helps visualize trigonometric functions because the coordinates of points on the unit circle correspond to the cosine and sine of angles. For example, for an angle θ, the x-coordinate represents cos(θ), and the y-coordinate represents sin(θ). This relationship allows for the extension of trigonometric functions to all angles, not just those in right triangles.
| 4. What are the inverse trigonometric functions, and why are they useful? | |
Ans.The inverse trigonometric functions are arcsine (sin⁻¹), arccosine (cos⁻¹), and arctangent (tan⁻¹). They are useful because they allow us to determine the angles when the values of the trigonometric functions are known. For instance, if we know that sin(θ) = 0.5, we can use arcsine to find that θ = sin⁻¹(0.5), which corresponds to the angles where the sine value is 0.5.
| 5. How do trigonometric identities facilitate the simplification of expressions in trigonometry? | |
Ans.Trigonometric identities are equations that involve trigonometric functions that are true for all values of the variables involved. They facilitate simplification of expressions by providing relationships such as the Pythagorean identity (sin²(θ) + cos²(θ) = 1) and angle sum identities (e.g., sin(α + β) = sin(α)cos(β) + cos(α)sin(β)). These identities help in solving equations, proving other identities, and simplifying complex trigonometric expressions.
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