TRIGONOMETRIC FUNCTIONS
Frequently Asked Questions
Trigonometrical functions are functions that relate an angle to ratios of sides of a right-angled triangle or to coordinates on the unit circle
Because each angle corresponds to a unique real value of sine, cosine, tangent, etc
An angle measured in radians can take any real value, positive or negative
Radian is the angle subtended at the center of a circle by an arc equal in length to the radius
There are p radians in 180 degrees
The domain of sin x and cos x is all real numbers
The range is from -1 to 1 inclusive
All real numbers except odd multiples of \(\pi/2\)
Periodicity means the function repeats its values after a fixed interval
The period is \(2\pi\)
The period is \(\pi)
Identities that hold true for all permissible values of \(x\), such as \(\sin^2 x + \cos^2 x = 1\)
Identities that relate trigonometric functions as reciprocals of each other
Identities expressing tan x and cot x as ratios of sine and cosine
Identities derived from the Pythagorean theorem involving sin, cos, and tan
The positivity or negativity of values depending on the quadrant
Sine is negative in the third and fourth quadrants
A mnemonic to remember which trigonometric functions are positive in each quadrant
Angles that differ by multiples of 90 degrees or 180 degrees
The acute angle formed between the terminal side of an angle and the x-axis
Using identities like sin(-x) = -sin x and cos(-x) = cos x
sin(90°-x)=cos x and similar relations
Relations involving angles whose sum is 180 degrees
Because cos x becomes zero at those points
A method of defining trigonometric functions using coordinates of a unit circle
They help analyze periodic behavior, amplitude, and phase
The maximum height of the wave from the mean position
Changes such as shifting, stretching, or reflecting the basic graphs
Horizontal displacement of a trigonometric graph
It is used in wave motion, oscillations, optics, and mechanics
Exact values help avoid approximation errors in exams
Common angles like \(0^\circ, 30^\circ, 45^\circ, 60^\circ, \text{ and \} 90^\circ\)
By simplifying one side to obtain the other side
Wrong sign selection, unit mismatch, and identity misuse
Trigonometric limits, derivatives, and integrals depend on it
It forms the base for calculus, vectors, and coordinate geometry
Learn identities, understand graphs, and practice problems daily
No, answers must be evaluated using exact values
It varies by board but forms a high-weightage foundational chapter
Identity proofs, value evaluation, graph-based, and conceptual questions
An exact value is a value expressed in surd or rational form without decimal approximation
Radians simplify formulas in calculus and provide a natural measure of angles
Their values repeat or change sign depending on periodicity and symmetry
Coterminal angles differ by integer multiples of \(\2pi\) and have the same trigonometric values
Symmetry helps determine even and odd nature of functions and simplifies graph sketching
Cos x is an even function while sin x and tan x are odd functions
By locating the angle in the correct quadrant and applying sign conventions
Expressing trigonometric functions of larger angles in terms of acute angles
It supports slope, angle, distance, and orientation calculations
Because it connects algebra, geometry, calculus, and real-world applications
