Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-6. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-6 with Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Class:	11th
Subject:	Mathematics
Chapter  :	Ch-6 Trigonometric Equations Angles of Section -A

Board	ISC
Writer	OP Malhotra
Publications	S.Chand Publications 2020-21

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-: Select Topics :- 

Exe-6

Chapter Test

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Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Angle
Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative.

Measuring Angles
There are two systems of measuring angles
Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is (1360)𝑡ℎ of a revolution, the angle is said to have a measure of one degree, written as 1°.
One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written as 1″
Thus, 1° = 60′ and 1′ = 60″

Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°.

Relation Between Radian and Degree
We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°.
2π radian = 360°.
Hence, π radian = 180°
or 1 radian = 57° 16′ 21″ (approx)
1 degree = 0.01746 radian

Trigonometric Functions 

Trigonometric ratios are defined for acute angles as the ratio of the sides of a right angled triangle. The extension of trigonometric ratios to any angle in terms of radian measure (real number) are called trigonometric function. The signs of trigonometric function in different quadrants have been given in following table.

	I	II	III	IV
Sin x	+	+	–	–
Cos x	+	–	–	+
Tan x	+	–	+	–
Cosec x	+	+	–	–
Sec x	+	–	–	+
Cot x	+	–	+	–

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Exe-6

Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 6 – 14

Question 1 :

Solve the following equations for 0 ≤ x ≤ 2 π

(i)

(ii)

(iii)

(iv)

(v)

Question 2 :

cos θ …………………… π/2

Question 3 :

……………………….

……………………….

………………………..

Question 12 :

tan θ …………………….. =0

…………………………

………………………..

Question 17 :

tan 2x ………………. x=0

………………………

………………………

Question 21 :

sin θ ……………….. √2

Question 27 :

sec θ …………….. = 4/3

Question 28 :

Find the smallest positive number …………………………………. a solution when x ∈ [0, 2π]

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Chapter Test

Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 6 -16

Question 1 :

Find the general value of θ which satisfies the equation sin² θ = 3/4

Question 2 :

Find the …………………….. = cos θ

Question 3 :

Solve ……………….. 360 degree

Question 4 :

Find the …………………. ≤ π.

Question 5 :

Solve ……………… =4

Question 6 :

Solve the equations ……………………………….

-: End of Trigonometric Equations Angles Solution :-

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