Educational

Sketch the Graph of f(x) = tan²x Question: Sketch the graph of the following function : \[ f(x)=\tan^2x \] Solution: We know that \[ \tan^2x=(\tan x)^2 \] Since square of tangent is always non-negative, the graph always lies above the x-axis. Whenever \[ \cos x=0 \] the tangent function becomes undefined. Thus vertical asymptotes occur […]

Sketch the Graph of f(x) = 2 sec πx Question: Sketch the graph of the following function : \[ f(x)=2\sec \pi x \] Solution: We know that \[ \sec\theta=\frac{1}{\cos\theta} \] Therefore \[ f(x)=2\sec \pi x=\frac{2}{\cos \pi x} \] The graph of secant is obtained from the graph of cosine. Vertical asymptotes occur wherever the cosine

Sketch the Graph of f(x) = cot 2x Question: Sketch the graph of the following function : \[ f(x)=\cot2x \] Solution: We know that \[ \cot\theta=\frac{\cos\theta}{\sin\theta} \] Therefore \[ f(x)=\cot2x \] The graph of cotangent decreases from \(+\infty\) to \(-\infty\) in each interval between two consecutive asymptotes. Whenever \[ \sin2x=0 \] the function becomes undefined.

Sketch the Graph of f(x) = 3 sec x Question: Sketch the graph of the following function : \[ f(x)=3\sec x \] Solution: We know that \[ \sec x=\frac{1}{\cos x} \] Therefore \[ f(x)=3\sec x=\frac{3}{\cos x} \] The graph of secant is obtained from the graph of cosine. Whenever \[ \cos x=0 \] the function

Sketch the Graph of f(x) = 2 cosec πx Question: Sketch the graph of the following function : \[ f(x)=2\cosec \pi x \] Solution: We know that \[ \cosec \theta=\frac{1}{\sin\theta} \] Therefore \[ f(x)=2\cosec \pi x=\frac{2}{\sin \pi x} \] The graph of cosecant is obtained from the graph of sine. Whenever \[ \sin \pi x=0

Sketch the Graphs of y = cos²x and y = cos x on the Same Axes Question: Sketch the graphs of the following curves on the same scale and the same axes : \[ y=\cos^2x \] \[ y=\cos x \] Solution: We know that \[ y=\cos x \] is the standard cosine curve having amplitude

Sketch the Graphs of y = cos x and y = cos(x/2) on the Same Axes Question: Sketch the graphs of the following curves on the same scale and the same axes: \[ y=\cos x \] \[ y=\cos\frac{x}{2} \] Solution: We know that \[ y=\cos x \] is the standard cosine curve having period \[

Sketch the Graphs of y = cos 2x and y = cos(x − π/4) on the Same Axes Question: Sketch the graphs of the following curves on the same scale and the same axes: \[ y=\cos2x \] \[ y=\cos\left(x-\frac{\pi}{4}\right) \] Solution: Consider the graph of \[ y=\cos2x \] Its amplitude is \(1\) and its period

Sketch the Graphs of y = cos x and y = cos(x − π/4) on the Same Axes Question: Sketch the graphs of the following curves on the same scale and the same axes: \[ y=\cos x \] \[ y=\cos\left(x-\frac{\pi}{4}\right) \] Solution: We know that \[ y=\cos x \] is the standard cosine curve. The

Sketch the Graph of g(x) = cos 2πx Question: Sketch the graph of the following trigonometric function : \[ g(x)=\cos 2\pi x \] Solution: We know that \[ y=\cos x \] is the standard cosine curve. In the function \[ y=\cos 2\pi x \] the angle is multiplied by \(2\pi\). Therefore the graph oscillates more