Hyperbolic Functions: Overview, Questions, Preparation

[Source: NCERT]

Trigonometric functions are the functions that are real and define the functions of a right-angled triangle. It relates the angles of a triangle with its sides. The six trigonometric functions are:

• Sine (sin)
• Cosine (cos)
• Tangent (tan)
• Secant (sec)
• Cosecant (cosec)
• Cotangent (cot)

Sine: The ratio of the side opposite to the angle with the hypotenuse of a right-angled triangle.

If x is the angle, then sin x = opposite side/hypotenuse.

Cosine: The side's ratio adjacent to the angle with the hypotenuse of a triangle.

cos x = adjacent side/hypotenuse

Tangent: The opposite side's ratio to the adjacent side of an angle in a right-angled triangle.

tan x = opposite side/adjacent side

Secant: The inverse of the cos function.

sec x = 1/cos x

Cosecant: The inverse of sin function.

cosec x = 1/sin x

Cotangent: The inverse of the cot function.  

cot x = 1/tan x

Pythagoras theorem

Pythagoras Theorem gives us the following identities:

sin2θ + cos2θ = 1

sec2θ = 1 + tan2θ

cosec2θ = 1 + cot2θ

Other identities

The sum and difference identities are given below:

sin(x+y) = sin(x).cos(y)+cos(x).sin(y)

sin(x–y) = sin(x).cos(y)–cos(x).sin(y)

tan(x+y) = [tan(x)+tan(y)]/[1-tan(x)tan(y)]

tan(x-y) = [tan(x)-tan(y)]/[1+tan(x)tan(y)]

cos(x+y) = cosx.cosy–sinx.siny

cos(x–y) = cosx.cosy+sinx.siny

Only sec and cos are even functions in trigonometry. The remaining are odd functions.

π and 2π are periodic cycles. 2π is the periodic cycle for sin, cos, cosec, and sec functions, whereas π is the periodic cycle for tan and cot functions.

You will be introduced to trigonometry concepts in Class X where it will carry a maximum weightage of 12 marks.

Class XI will give you a more in-depth insight into this topic. Together with trigonometric equations, this topic carries a weightage of 23 marks in Class XI.

You will learn about inverse trigonometric functions in Class XII, and it will carry a weightage of 8 marks.