Class 11 Maths Ch-3 Trigonometric Functions

NCERT Solutions of Class 11 Maths Ch-3 Trigonometric Functions

Exercise 3.1

Question 1:
Find the radian measures corresponding to the following degree measures:
(i) 25^o \(\quad \quad\) (ii) -47^o 30′ \(\quad \quad\) (iii) 240^o \(\quad \quad\) (iv) 520^o

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Question 2:
Find the degree measures corresponding to the following radian measures (Use π = \(\frac{22}{7}\))
(i) \(\frac{11}{16}\) \(\quad \quad\) (ii) -4 \(\quad \quad\) (iii) \(\frac{5\pi}{3}\) \(\quad \quad\) (iv) \(\frac{7\pi}{6}\)

Question 3:
A wheel makes 360 revolutions in one minute. Through how many radians doesit turn in one second?

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 = \(\frac{22}{7}\)).

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.

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.

Question 7:
Find the angle in radian through which a pendulum swings if its length is 75 cm and th e tip describes an arc of length
(i) 10 cm \(\quad \quad\) (ii) 15 cm \(\quad \quad\) (iii) 21 cm

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NCERT Solutions of Class 11 Maths Ch-3 Trigonometric Functions

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Exercise 3.2

Find the values of other five trigonometric functions in Exercises 1 to 5.

Question 1:
\(\cos {x}\) = – \(\frac{1}{2}\), x lies in third quadrant.

Question 2:
\(\sin {x}\) = \(\frac{3}{5}\), x lies in third quadrant.

Question 3:
\(\cot {x}\) = \(\frac{3}{4}\), x lies in third quadrant.

Question 4:
\(\sec {x}\) = \(\frac{13}{5}\), x lies in third quadrant.

Question 5:
\(\tan {x}\) = – \(\frac{5}{12}\), x lies in third quadrant.

Find the values of the trigonometric functions in Exercises 6 to 10

Question 6:
\(\sin(765^\circ)\)

Question 7:
\(\csc\left(-1410^\circ\right)\)

Question 8:
\(\tan{\frac{19\pi}{3}}\)

Question 9:
\(\\sin\left(\frac{-11\pi}{3}\right)\)

Question 10:
\(\cot\left(\frac{-15\pi}{4}\right)\)

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NCERT Solutions of Class 11 Maths Ch-3 Trigonometric Functions

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Exercise 3.3

Prove that:

Question 1:
\(\sin^2 \frac{\pi}{6} + \cos^2 \frac{\pi}{3} – \tan^2 \frac{\pi}{4} = – \frac{1}{2}\)

Question 2:
\(2\sin^2 \frac{\pi}{6} + \csc^2 \frac{7\pi}{6} \cos^2 \frac{\pi}{3} = \frac{3}{2}\)

Question 3:
\(\cot^2 \frac{\pi}{6} + \csc^2 \frac{5\pi}{6} + 3\tan^2 \frac{\pi}{6} = 6\)

Question 4:
\(2\sin^2 \frac{3\pi}{4} + 2\cos^2 \frac{\pi}{4} + 2\sec^2 \frac{\pi}{3} = 10\)

Question 5:
Find the value of:
(i) \(\sin 75^\circ\) \(\quad\quad \quad\) (ii) \(\tan 15^\circ\)

Prove the following:

Question 6:

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NCERT Solutions of Class 11 Maths Ch-3 Trigonometric Functions

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Miscellaneous Exercise on Chapter 3

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NCERT Solutions of Class 11 Maths Ch-3 Trigonometric Functions

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