CBSE Class XI

Question 4:

Answer

Question 3:

Answer

Question 2 :

Answer

Question 1:

Answer

Question 10:

Find the value of the trigonometric function cot(−15π/4)

Answer

It is known that value of cot x repeat after an interval of n or 180°.

Question 9:

Find the value of the trigonometric function sin(−11π/3)

Answer

It is known that the value of sin x repeat an interval of 2n or 360°.

Question 8:

Answer

It is known that the values of tan x repeat after an interval of n or 180°.

Question 7:

Find the value of the trigonometric function cosec (−1410°)

Answer

∴ cosec(−1410°) = cosec(−1410° + 4 × 360°)

                                  =cosec(−1410° + 1440°)

                                  = cosec 30° = 2

Question 6:

Find the value of the trigonometric function sin 765°

Answer

Question 5:

Find the values of other five trigonometric functions if tan x = −5/12, x lies in second quadrant.

Answer

Question 4:

Find the values of other five trigonometric functions if sec x = 13/5, x lies in fourth

quadrant.

Answer

Question 3:

Find the values of other five trigonometric functions if cot x = 3/4, x lies in third quadrant.

Answer

Since x lies in the 3^rd quadrant, the value of sec x will be negative.

Question 2:

Find the values of other five trigonometric functions if sin x = 3/5, x lies in second quadrant.

Answer

Since x lies in the 2^nd quadrant, the value of cos x will be negative

Question 1:

Find the values of other five trigonometric functions if cos x = −1/2, x lies in third quadrant.

Answer

Since x lies in the 3^rd quadrant, the value of sin x will be negative.

Question 7:

Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length

(i) 10 cm               (ii) 15 cm                       (iii) 21 cm

Answer

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = l/r

It is given that r = 75 cm

(i) Here, l = 10 cm

Question 6:

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Answer

Let the radii of the two circles be 60° and 75°. Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r₁, while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r₂.

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = l/r or l = rθ

Thus, the ratio of the radii is 5:4.

Question 5:

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Answer

Diameter of the circle = 40 cm

∴Radius (r) of the circle = 40/2 cm = 20 cm

Let AB be a chord (length = 20 cm) of the circle.

In ΔOAB, OA = OB = Radius of circle = 20 cm Also, AB = 20 cm

Thus, ΔOAB is an equilateral triangle.

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = 1/r.

Thus, the length of the minor arc of the chord is 

Question 4:

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm(Use π = 22/7).

Answer

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then

θ = 1/r

Therefore, forr = 100 cm, l = 22 cm, we have

Thus, the required angle is 12°36′.

Question 3:

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Answer

Number of revolutions made by the wheel in 1 minute = 360

∴Number of revolutions made by the wheel in 1 second = 360/60 = 6

In one complete revolution, the wheel turns an angle of 2π radian.

Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian,

i.e., 12 π radian

Thus, in one second, the wheel turns an angle of 12π radian.

Question 2:

Find the degree measures corresponding to the following radian measures

(use π = 22/7)

(i)      11/16          (ii)     −4     (iii)    5π/3            (iv)    7π/6

Answer

(i) 11/16

We know that π radian = 180°

(ii) −4

We know that π radian = 180°

(iii) 5π/3

 We know that π radian = 180°

(iv) 7π/6

We know that π radian = 180°