Today is our topic of discussion Trigonometry exercises 8.3 .
Trigonometry exercises 8.3
1. If sinA=1/√2. then find the value of sin 2A.
1) 1/√2
2) 1/2
3) 1
4) √2
2. In which quadrant the angle -300° lies?
1) First
2) Second
3) Third
4) Fourth
3. If sineθ + coseθ = 1, then the value of θ is
(i) 0°
(ii) 30°
(iii) 90°
Which one of the followings is correct?
1) i
2) ii
3) i and ii
4) i and iii
4. From the figure –
(i) tanθ = 4/3
(ii) sinθ = 5/3
(iii) cos²θ = 9/25
Which one of the following is correct?
1) i and ii
2) i and iii
3) ii and iii
4) i, ii and iii
Answer no. 5 and 6 in accordance with the following figure:
5. sinB + cosC = ?
1) 2b/a
2) 2a/b
3) a²+b²/ab
4) ab/a²+b²
6. What is the value of tan B?
1) a/a²-b²
2) b/a²-b²
3) a/√a²-√b²
4) b/√a²-√b²
7. Find the value of
8. Prove that,
9. Find the value of
10. If θ=π/3 then prove the following identities:
1) sin2θ = 2sinθcosθ= (2tanθ)/(1 + tan² θ)
2) cos3θ = 4cos³ θ – 3cosθ
3) sin3θ = 3sinθ – 4sin³θ
4) tan2θ = (2tanθ)/(1 – tan²θ)
11. Find the value of a satisfying the given conditions:
1) cotα = – √3, (3π)/2 < α <π
2) cosα = – 1/2, π/2 < α < (3π)/2
3) sinα = – √3/2, π/2 < α < 3π/2
4) cotα = – 1 , π < α < 2α
12. Solve : (where 0 < θ < π/2 )
1) 2cos² θ = 1 + 2sin² θ
2) 2sin^2θ – 3cosθ = 0
3) 6sin²θ – 11sinθ + 4 = 0
4) tanθ + cotθ = pm sqrt 3
5) 2sin²θ + 3cosθ = 3
13. Solve (where 0 < θ < 2π
1) 2sin²θ + 3cosθ = 0
2) 4(cos²θ + sinθ ) = 5
3) cot²θ + cosec²θ = 3
4) tan²θ + cot²θ = 2
5) sec²theta + tan²theta = 5/3
6) 5cosec²theta – 7cot theta*co * sec(theta) – 2 = 0
7) 2sin cost sinx (0 ≤ x ≤ 2π) =
14. Radius of the Earth is 6440 km. Dhaka and Panchagar make 3.5 deg angle at the centre of the Earth. A person wants to enjoy scenic natural beauty of Panchagar in the winter. He reached Panchagar with a vehicle having a wheel of diameter 0.84 m.
1) What is the angle in radians Dhaka and Panchagar make at the centre of the Earth?
2) What is the distance between Dhaka and Panchagar?
3) How many revolutions will the wheel make while travelling to Panchagar from Dhaka?
15.
1) In figure ABC is a circular wheel and length of the arc AB is 25 c.m. Find the value of 0. What distance will the wheel cover in a single rotation?
2) What is the speed of the wheel ABC if it revolves 5 times in a second.
3) In the figure find the value of sin theta from triangle ΔBOD , to prove that, tan theta + secθ = x
16. In a right angled triangle if the length of smallest side is 7c.m. and the smallest angle is 15° , then what is the length of hypotenuse?
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