Trigonometric Functions Class 11 Notes - Chapter 3

Trigonometry deals with the relationship between the angles and sides of the triangles. It is derived from ‘trigon’ and ‘metron’ (Greek words), which means the measurement of the sides of a triangle. An angle is the measurement of the rotation of a revolving line w.r.t to a fixed line. The angle has +ve or -ve values depending on its rotation [-ve for clockwise rotation and +ve for anti-clockwise rotation].

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Conventions for Angle Measurements

• Sexagesimal system: In this system, the angle is measured in degrees. 1° = 60′ and 1′ = 60″.
• Circular system: In this system, the angle is measured in radians.

1 radian = Angle subtended at the centre of a circle by an arc of length equal to the radius of the circle.

Relationships between Radian and degree

1 Radian = 180/π degree and 1 Degree = π/180 radian

Functions of negative angles (A)

• sin (-A) = – sinA,
• cosec (-A) = -cosec A,
• tan (-A) = – tan A,
• cos (-A) = cos A,
• cot (-A) = -cot A,
• sec (-A) = sec A.

To get more details on Trigonometry Angles, visit here.

Trigonometric formulas of compound angles

The resultant of the sum or differences of two or more angles is known as the compound angle that results in trigonometric identities, as mentioned below.

• sin (C + D) = cosC sinD + sinC cosD
• sin (C – D) = sinC cosD – cosC sinD
• cos (C + D) = cosC cosD – sinC sinD
• cos (C – D) = sinC sinD + cos C cosD
• 2 sinC cosD = sin (C + D) + sin (C – D)
• 2 cosC sinD = sin (C + D) – sin (C – D)
• 2 cosC cosD = cos (C + D) + cos (C – D)
• 2 sinC sinD = cos (C – D) – cos (C + D)

To get more details on Trigonometric Ratios of Compound Angles, visit here.

Important Trigonometric equations

The equations involving trigonometric functions are known as trigonometric equations. These trigonometric equations are termed identities if all the values of unknown angles for which the functions are defined are satisfied. The solutions of trigonometric expressions for which 0 ≤ θ < 2π is known as the principal solution. The equations involving integer ‘n’, which provides all the possible solutions of a trigonometric expression, is known as the general solution.

Trigonometric Equations General Solution

If sin A = sin P, then A = nπ + (–1)nP for n ∈ Z gives the general solution of the given trigonometric equation. If cos A = cos P, then A = 2nπ ± P, n ∈ Z gives the general solution of the given trigonometric equation. If tan A = tan P or cot A = cot P, then A = nπ + P, n ∈ Z, gives a general solution for both the given trigonometric equations.

The general value of A satisfying equations sin 2A = sin 2P, cos 2A = Cos 2P and tan 2A = tan 2P are given by A = nπ ± P. The general value of A satisfying equations sin A = sin P and cos A = cos P simultaneously is given by A = 2nπ + P, n ∈ Z.

Also Read:  NCERT Solutions for Class 11 Maths Chapter 3

Trigonometric Functions Class 11 Practice Questions

1. Determine the value of [-cos (45° + (-θ))] + sin (θ + 45°).
2. Evaluate tan 3P + tan 2P – tan P
3. Find the minimum value of 4cosx – 5sinx – 87.
4. If tan θ = 3 and θ lies in the 4th quadrant, then find the value of sin θ.
5. Find the value of sin1° sin2° sin3° . . . . . . . . . sin 179°.
6. Find the general solution of trigonometric equation (-3)sin2x + sin3x = 3 cos2x + cosx – cos3x
7. Determine the general value of θ, If cosθ + sinθ = 1.
8. If 3tan (θ – 20°) = tan (θ + 20°), 0° < θ < 90°, then find the value of θ.
9. Solve the equation sin 2θ + sin θ + sin 3θ = 0.
10. Determine the value of tan 19° + tan 127° – tan 163° – tan 21°.

Also Refer: NCERT Exemplar for Class 11 Maths Chapter 3

Related Links:

• Trigonometric formulas
• Trigonometric Ratios
• Trigonometric Functions
• Inverse Trigonometric Functions
• Graphical Representation Of Inverse Trigonometric Function

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