# Ex. No. 4.1

1. Draw the figure and write the answers :

(i) For the angle in standard position if the initial arm rotates 220º in clockwise direction then terminal arm is in which quadrant ? [Ans.] [VIDEO]

(ii) For the angle in standard position if the initial arm rotates 25º in anticlockwise direction then terminal arm is in which quadrant? [Ans.] [VIDEO]

(iii) For the angle in standard position if the initial arm rotates 305º in anticlockwise direction then terminal arm is in which quadrant ? [Ans.] [VIDEO]

2. The terminal arm is in II quadrant, what are the possible angles ? [Ans.] [VIDEO]

3. The terminal arm is on negative Y-axis, what are the possible angles ? What can you say about this angle ? [Ans.] [VIDEO]

Ex. No. 4.2

TRIGONOMETRIC FORMULA

1. Find the trigonometric ratios in standard position whose terminal arm passes through the points :

(i) (4, 3) [Ans.] [VIDEO]

(ii) (5, – 12) [Ans.]

(iii) (– 24, – 7) [Ans.]

(iv) (–1 , √3) [Ans.] [VIDEO]

(v) (1, – 1) [Ans.]

(vi) (– 2, – 3) [Ans.]

2. If the angle θ = – 60º, find the value of sin θ , cos θ, sec θ  and tan θ. [Ans.] [VIDEO]

3. Find where the angle lies if the terminal arm passes through :

(i) (5, – 7) [Ans.] [VIDEO]

(ii) (– 8, 1) [Ans.] [VIDEO]

(iii) (– 3, – 3) [Ans.] [VIDEO]

(iv) (0, 2) [Ans.] [VIDEO]

4. If cos θ = 7/25 and θ is in the fourth quadrant, find the other five trigonometric ratios. [VIDEO]

Ex. No. 4.3

1. If sin θ  = 5/13 . where θ  is an acute angle, find the value of other trigonometric ratios using identities. [Ans.] [VIDEO]

2. If cot θ  = - 7/24, then find the values of sin θ  and sec θ, If θ is in IV quadrant. [Ans.] [VIDEO]

3. 3 sin α – 4 cos α = 0, then find the values of tan α , sec α and cosec α, where α is an acute angle. [Ans.] [VIDEO]

4. If tan θ  = 1, then find the value of (sinθ  + cos θ) ÷  (secθ  + cosecθ ), where θ is an acute  angle.  [Ans.] [VIDEO]

5. If sec α = 2/√3,  , then find the value of (1-cosec α)/(1+cosec α) , where α  is in IV quadrant. [Ans.] [VIDEO]

6. Find the possible values of sin x if 8 sin x – cos x = 4. [Ans.] [VIDEO]

7. Prove the following :

(i) √((1-cos A)/(1+cos A)=cosec A-  cot A)  [Ans.]  [VIDEO]

(ii) √((cosec x-1)/(cosec x+1))=1/(sec x+tan x)  [Ans.]

(iii) sec2θ + cosec2θ = sec2θ .cosec2θ   [Ans.] [ VIDEO]

(iv) sec6x – tan6x = 1 + 3 sec2x  . tan2[Ans.] [VIDEO]

(v) tanθ/(secθ+1)+(secθ+1)/tanθ = 2 cosecθ  [Ans.]

(vi) (1+sinA)/cosA = (1+sinA+cosA)/(1+cos A-sinA )  [Ans.]

(vii) tanA/(secA-1) = (tanA+sec A+1)/(tan A+sec A-1)  [Ans.]

(viii) √(sec2 θ+cosec2 θ)= tanθ + cot θ  [Ans.]

(ix) 1/(cosec A-cot A )-1/sinA=1/sinA-1/(cosec A+cot A) [Ans.]

(x) If  tan A + 1/tan A = 2, Show that tan2A + 1/tan2A = 2. [Ans.]

8. Eliminate θ, if

(i) x = a secθ, y = b tanθ [Ans.]

(ii) x = 2 cosθ – 3 sin θ , y = cos θ + 2 sin θ [Ans.]

(iii) x = 3 cosec θ  + 4 cot θ, y = 4 cosec θ – 3 cot θ [Ans.]

Ex. No. 4.4

1. For a person standing at a distance of 80 m from a church, the angle of elevation of its top is of measure 45º. Find the height of the church. [Ans.]  [VIDEO]

2. From the top of a lighthouse, an observer looks at a ship and find the angle of depression to be 60º. If the height of the lighthouse is 90 metres then find how far is that ship from the lighthouse ? ( √3 = 1.73). [Ans.]  [VIDEO]

3. Two buildings are in front of each other on either side of a road of width 10 metres. From the top of the first building, which is 30 metres high, the angle of elevation of the top of the second is 45º. What is the height of the second building ? [Ans.] [VIDEO]

4. 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. [Ans] [VIDEO]

5. A tree is broken by the wind. The top struck the ground at an angle of 30º and at a distance of 30 m from the root. Find the whole height of the tree. ( √3 = 1.73) [Ans.]   [VIDEO]