IB Mathematics Analysis and Approaches Question Type 4: Applying Transformation to Trigonometric Functions Under a Specific Domain Exercises

Given $y=-\sin \left(2x+\frac{\pi }{3}\right)$, find one interval of length one period within $-\pi <x<\pi$ and list all $x$ in that interval where $y=0$.

For $y=\sin \left(3x-\frac{\pi }{2}\right)$, find the phase shift and the first positive $x$-intercept in $-\pi <x<\pi$.

Identify the amplitude and period of $y=2\sin \left(\frac{x}{3}\right)$ on the domain $-\pi <x<\pi$.

Find the period and midline of $y=4\sin \left(\frac{x}{4}\right)-3$.

Solve $\sin \left(\frac{x}{2}\right)+2=0$ for $-\pi <x<\pi$.

For $y=5\sin (3x-\pi )+2$, find the amplitude, period, and equation of the principal axis.

Solve the equation $2\sin \left(\frac{x}{3}\right)-1=0$ for $-\pi <x<\pi$.

Determine the maximum and minimum values of $y=3\cos (2x+\pi )$ on $-\pi <x<\pi$.

Determine the range and period of $y=-2\cos \left(\frac{x}{6}\right)+4$.

Write the function obtained by shifting $y=2\sin \left(\frac{x}{3}\right)$ up by 1 unit, and determine its new maximum value.

Find all $x$-intercepts of $y=2\sin \left(\frac{x}{3}\right)$ in the interval $-\pi <x<\pi$.

Solve $5\sin (3x-\pi )+2=2$ for $-\pi <x<\pi$.