Educational

Sketch the Graphs of y = sin x and y = sin(x + π/4) on the Same Axes Question: Sketch the graphs of the following pairs of functions on the same axes: \[ f(x)=\sin x \] \[ g(x)=\sin\left(x+\frac{\pi}{4}\right) \] Solution: We know that \[ y=\sin x \] is the standard sine curve. Now consider \[ […]

Sketch the Graph of f(x) = 2 sin πx for 0 ≤ x ≤ 2 Question: Sketch the graph of the following function : \[ f(x)=2\sin \pi x,\quad 0 \le x \le 2 \] Solution: We know that the graph of \[ y=\sin x \] is a standard sine curve. In the function \[ y=2\sin

Sketch the Graphs of u(x) = sin²x and v(x) = |sin x| for 0 ≤ x ≤ 2π Question: Sketch the graphs of the following functions : \[ u(x)=\sin^2x,\quad 0 \le x \le 2\pi \] \[ v(x)=|\sin x|,\quad 0 \le x \le 2\pi \] Graph of \(u(x)=\sin^2x\) Solution: Since \[ u(x)=\sin^2x \] therefore all values

Sketch the Graph of θ(x) = sin(x/2 − π/4) for 0 ≤ x ≤ 4π Question: Sketch the graph of the following function : \[ \theta(x)=\sin\left(\frac{x}{2}-\frac{\pi}{4}\right), \quad 0 \le x \le 4\pi \] Solution: We know that the graph of \[ y=\sin x \] is a standard sine curve. In the function \[ y=\sin\left(\frac{x}{2}-\frac{\pi}{4}\right) \]

Sketch the Graph of ψ(x) = 4 sin 3(x − π/4) for 0 ≤ x ≤ 2π Question: Sketch the graph of the following function : \[ \psi(x)=4\sin 3\left(x-\frac{\pi}{4}\right),\quad 0 \le x \le 2\pi \] Solution: We know that the graph of \[ y=\sin x \] is a standard sine curve. In the function \[

Sketch the Graph of Φ(x) = 2 sin(2x − π/3) for 0 ≤ x ≤ 7π/5 Question: Sketch the graph of the following function : \[ \Phi(x)=2\sin\left(2x-\frac{\pi}{3}\right),\quad 0 \le x \le \frac{7\pi}{5} \] Solution: We know that the graph of \[ y=\sin x \] is a standard sine curve. In the function \[ y=2\sin\left(2x-\frac{\pi}{3}\right) \]

Sketch the Graph of h(x) = 2 sin 3x for 0 ≤ x ≤ 2π/3 Question: Sketch the graph of the following function : \[ h(x)=2\sin 3x,\quad 0 \le x \le \frac{2\pi}{3} \] Solution: We know that the graph of \[ y=\sin x \] is a standard sine curve. In the function \[ y=2\sin 3x

Sketch the Graph of g(x) = 3 sin(x − π/4) for 0 ≤ x ≤ 5π/4 Question: Sketch the graph of the following function : \[ g(x)=3\sin\left(x-\frac{\pi}{4}\right), \quad 0 \le x \le \frac{5\pi}{4} \] Solution: We know that the graph of \[ y=\sin x \] is a standard sine curve. In the function \[ y=3\sin\left(x-\frac{\pi}{4}\right)

Sketch the Graph of f(x) = 2 sin x for 0 ≤ x ≤ π Question: Sketch the graph of the following function : \[ f(x)=2\sin x,\quad 0 \le x \le \pi \] Solution: We know that the graph of \(y=\sin x\) is a sine curve. Since the function is \[ y=2\sin x \] therefore

Question \[ \text{If } \frac{3\pi}{4}<x<\pi, \] \[ \sqrt{\cosec^2x+2\cot x} \] \[ \text{is equal to} \] Solution Using identity \[ \cosec^2x=1+\cot^2x \] Therefore, \[ \cosec^2x+2\cot x \] \[ =1+\cot^2x+2\cot x \] \[ =(\cot x+1)^2 \] Hence, \[ \sqrt{\cosec^2x+2\cot x} = |\cot x+1| \] Since \[ \frac{3\pi}{4}<x<\pi \] \(x\) lies in second quadrant and \[ -1<\cot x<0