Trigonometry Class 10


Trigonometry: Introductory Videos


Introduction to Trigonometry (For All Boards): Class 10: Part 1

In this section we will try to understand: 1) What is trigonometry and 2) the basic terms involved in the trigonometry like sin, cos, tan, cot, sec and cosec.
https://www.youtube.com/watch?v=lCeer92qsHs

Introduction to Trigonometry (For All Boards): Class 10: Part 2

In this video, I am trying to explain the basic meaning and definition of sin, cos, tan, cot, sec and cosec.


Introduction to Trigonometry (For All Boards): Class 10: Part 3

In this video you will learn how to remember trigonometric ratios.

Introduction to Trigonometry (For All Boards): Class 10: Part 4

In this video you will learn about trigonometric table. You will also learn the technique to remember the values inside the table.


Introduction to Trigonometry (For All Boards): Class 10: Part 5

Learn the technique to know how to remember trigonometric table.
https://www.youtube.com/watch?v=_iFU5MtYyJY


Introduction to Trigonometry (For All Boards): Class 10: Part 6

What you will learn in this video? You will learn about effect on values of trigonometric ratios in quadrant system.


Introduction to Trigonometry (For All Boards): Class 10: Part 7

Let us see how do sin, cos, tan, cot, sec, cosec behave in different quadrants.

Introduction to Trigonometry (For All Boards): Class 10: Part 8

What you will learn in this video? You will learn about trigonometric identities. You will also learn how to derive trigonometric identities.

Trigonometry Problems:


1) If tanѳ =2, where ѳ is an acute angle find the values of other trigonometric ratios using the adentities.
    https://www.youtube.com/watch?v=dI_qEPAbVYI

2) If cos Ѳ = 1/√2 , where Ѳ is an acute angle then find the values (1-tanѳ+secѳ)/(1-cotѳ+cosecѳ).
https://www.youtube.com/watch?v=3NJZvOaHelQ

3) Find the possible values of tanx, if (cos^2)x +5sinx. cosx = 3.
https://www.youtube.com/watch?v=CIv-epYoWs0

4) Show that √((1+sinx)/(1-sinx)) = secx+tanx
https://www.youtube.com/watch?v=OFK9t0wlHtk

 5) Show that sinѳ/(1+cosѳ) = (1-sinѳ-cosѳ)/(sinѳ-1-cosѳ)
https://www.youtube.com/watch?v=cMu1D0edlFE

6) Eliminate Ѳ, if x = r cos ѳ, y = r sinѳ.
https://www.youtube.com/watch?v=19ApM3r_AGQ

7) Eliminate Ѳ, If x = a cosecѳ + b cot ѳ, y = a cosecѳ – b cotѳ

8) If sin Ѳ = 5/(13,) , where ѳ is an acute angle, find the value of other trigonometry ratios using identities.

9) If cotѳ = - 7/(24,) then find the values of sinѳ and secѳ, ѳ is in IV quadrant.

10) 3 sin α- 4 cosα = 0, then find the values of tan α, sec α, and cosec α where α is an acute angle.

11) If tan α = 1, then find the values of (sinѳ+cosѳ)/(secѳ+cosecѳ) ,where ѳ is an acute angle.

12) If sec α = 2/√3 , then find the values of (1-cosecα)/(1+cosecα) , where α is in IV quadrant

13) Find the possible values of sinx if 8sinx–cosx =4.

14) Prove that following
√((1-cosA)/(1+COSA)) = cosec A – cot A.
https://www.youtube.com/watch?v=KRtZqMxS_Xk
15) Prove that: √((cosecx-1)/(cosecx+1)) = 1/(secx+tanx)
https://www.youtube.com/watch?v=yCtvcD9P1NU

16) Prove that: (sec^2)ѳ + (cosec^2)ѳ = (sec^2)ѳ * (cosec^2)ѳ
https://www.youtube.com/watch?v=Qt1m6Y4rsvQ

17) Prove that (sec^6)x - (tan^6)x = 1 + 3(sec^2)x (tan^2)x
https://www.youtube.com/watch?v=WR7zJXAxC-s

18) Prove that: (tan ѳ)/(secѳ+1) + (secѳ+1)/(tan ѳ) = 2 cosecѳ.
https://www.youtube.com/watch?v=L544mfpwwAk

19) Prove that following:
(1+sinA)/cosA = (1+sinA+cosA)/(1+cosA-sinA).

20) Prove that tanA/(secA-1)= (tanA+secA+1)/(tanA+secA-1)

21) Prove that: √(sec^2ѳ + cosec^2ѳ)= tanѳ + cotѳ.

22) Prove that 1/(cosecA-cotA) - 1/sin = 1/sinA - 1/(cosecA+cotA)
https://www.youtube.com/watch?v=k6Anh_TtFFk

23) If tan A + 1/tanA = 2, show that : (tan^2)A + 1/((tan)^2 A) = 2
https://www.youtube.com/watch?v=jARfTM7eS_M

24) Eliminate ѳ, if x = a sec ѳ, y =b tan ѳ
https://www.youtube.com/watch?v=k8gvBUZg18U

25) Eliminate ѳ, x = 2cos ѳ –3sin ѳ, y = cosѳ + 2sinѳ
https://www.youtube.com/watch?v=-gTVJpmYMw0

26) Eliminate ѳ, x = 3 cosecѳ + 4 cotѳ, y = 4 cosecѳ – 3 cotѳ
https://www.youtube.com/watch?v=bzERU-RKaKk

27) A boys is at a distance of 60 meters from a tree makes an angle of elevation of 60° which the top of the tree. What is the height of the tree? (√3 = 1.73)
https://www.youtube.com/watch?v=tBdLQUoJ5gM

28) From a point on the roof of a house, 11 meters high it is observed that the angles of depression of the top and foot of a lamp post are 30° and 60° respectively. What is the height of the lamp post?
https://www.youtube.com/watch?v=c5Du7c_N65E

29) Two person on the same side of a tall building notice the angle of elevation to the top of a building be 30° and 60° respectively. If the height of the building is 72m, find the distance between two person.
https://www.youtube.com/watch?v=DWXjs6edayo

30) A ship of height 24 m is sighted from a light house. From the top of the light house, the angle of depression to the top of the mast and base of the ship is 30° and 45° respectively. How far is the ship from the lighthouse?
https://www.youtube.com/watch?v=W62dw5xEprI

31) The angle of elevation of a cloud as seen from a point 400 meters above a take is 30° and the angle of Its reflection in the lake is 45°. Find the height of the cloud above the lake. (√3 = 1.73)
https://www.youtube.com/watch?v=eV_i9JAa_9w

32) For a person standing at a distance of 80 m from a church , the angle of elevation of its top is of measure 45°. Find the height of the church.
https://www.youtube.com/watch?v=Zwpcaqfijv0

33) From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60°.If the height of the lighthouse is 90 metres then find how far is that ship from the lighthouse? (√3 = 1.73)
https://www.youtube.com/watch?v=MpKLDl4PWAg

34) Two buildings are in front of each other on either of side of a road of width 10 metres. From the top of the first building which is 30 meters high, the angle of elevation of the top of the second is 45°. What is the height of the second building?
https://www.youtube.com/watch?v=7xBXvg7E7gA

35) Two poles of height 18 metres and 7 metres are erected on the ground . A wire of length 22 metres tied to the top of the poles . Find the angle made by the wire with the horizontal.
https://www.youtube.com/watch?v=mJOw-el1Btc

36) A tree is broken by the wind. The top struck the ground at an angle of 30° and at distance of 30m from the root. Find the whole height of the tree. (√3 = 1.73)
https://www.youtube.com/watch?v=A4l40tiQbOs

37) A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string . (√3 = 1.73 )
https://www.youtube.com/watch?v=foJ55OD4l4g

38) If the terminal arm passes through the point (1, -1) making an angle ѳ find the values of secѳ.
https://www.youtube.com/watch?v=AK-QeH8gY8k

39) If the terminal arm passes through (4, -7) find all the trigonometry ratios.
https://www.youtube.com/watch?v=qQHtWj4Pl6M

40) If the angle ѳ= -60, find cosѳ and cosecѳ
https://www.youtube.com/watch?v=MomWstsmHwY

41) Show that: tanѳ/(1-cotѳ ) + cot⁡ѳ/(1-tanѳ) =1+ secѳ. cosecѳ.

42) Show that : (sinѳ-cosѳ+1)/(sinѳ+cosѳ-1) = 1/(secѳ-tanѳ)

43) Show that : (cos^2)ѳ/(1-tanѳ) + (sin^3)ѳ)/(sinѳ-cosѳ) = 1+sinѳ cosѳ.

44) If 3(tan^2)ѳ - 4√3tanѳ + 3=0, find the acute angles Ѳ .

45) Find the possible values of cosx if cotx + cosecx = 5

46) If tanѳ+sinѳ = m and tanѳ –sinѳ = n, show that m^2- n^2 = 4√mn

47) If secѳ + tanѳ = p, show that (p^2-1)/(p^2+1) = sin ѳ.

48) If x=a sinѳ, y=b tanѳ then prove that a^2/x^2 – b^2/y^2 = 1

49) If acosѳ + bsinѳ=m and asinѳ – bcosѳ=n, prove that a^2 +b^(2 )= m^2 + n^2

50) If sin ѳ + (sin^2) ѳ = 1, prove that (cos^2) ѳ + (cos^4) ѳ = 1

51) √3tanѳ=3sinѳ, find the value of (sin^2) ѳ - (cos^2) ѳ, where Ѳ ≠ Ѳ

52) A tree 12m high is broken by the wind in such a way that its top touches the ground and makes an angle 60° with the ground. At what height from the bottom the tree is broken by the wind ?
( √3 = 1.73)

53) A Person standing on the bank of a river observes that the angle of elevation of the top of tree standing on the opposite bank 60°. When he moves 40 m away from the bank. He finds the angles of elevation to be 30° . finds the height of the tree width of the river. ( √3 = 1.73) (PART 1) https://www.youtube.com/watch?v=g5Eg9oz_S3o
      (PART 2) https://www.youtube.com/watch?v=Q4qB7ctb8KA
      (PART 3) https://www.youtube.com/watch?v=qLr7MUdjxfU

*54) The angle of elevation of a cloud from a point 60m above a lake is 30° and the angle of the depression of the reflection of cloud in the lake is 60°. Find the height of the cloud.

55) A man on a cliff observes a boat at an angle of depression 30°, which is sailing towards the point of the shore immediately beneath him, there minutes later the angle of depression of the boat is found to be 60°. Assuming that the boat sail at a uniform speed determine how much more time it will take to reach the shore.

56) A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tide to a peg at the ground. The height of the pole is 12 m and the angle made by the rope with the ground level is 30°. Calculate the distance covered by the artist in climbing to the top of the pole.

57) A bird was flying in a line parallel to the ground from at height of 2000 meters. Tom, standing In the middle of the field , he observed the bird making an angle of elevation 30°. After 3 minutes, he again observed it with an angle of elevation of 45°. Find the speed of the bird in kilometers per hour. ( √3 = 1.73 )


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