Graphs of Trigonometric Functions - Problem Solving Practice Problems Online

Consider the intersection points of the two functions $\begin{aligned} y&=\cos 26x \\ y&=k, \; (-1<k<0) \end{aligned}$ in the domain $0 \leq x \leq \frac{3}{26}\pi$ . If the $x$ -coordinates of those points are $\alpha$ , $\beta$ and $\gamma$ in an ascending order, the value of $\alpha+2\beta+\gamma$ can be expressed as $\frac{a}{b}\pi$ , where $a$ and $b$ are coprime positive integers. What is the value of $a+b$ ?

If the minimum and maximum value of $y=\left| \sin x-\frac{1}{10}\right|+18$ are $a$ and $b$ , respectively, what is the value of $a+10b$ ?

Consider the function $f(x)=a \cos bx+c,$ where $a>0$ and $b>0$ . If the period of $f(x)$ is $\frac{2}{5}\pi$ , the maximum value of $f(x)$ is $13$ , and $f(\pi)=-11$ , what is the value of $abc$ ?

Consider the function $f(x)=a|\cos bx|+c,$ where $a>0$ and $b>0$ . If the period of $f(x)$ is $\frac{\pi}{7}$ , the maximum value is $27$ , and $f\left(\frac{\pi}{21}\right)=18$ , what is the value of $a+b+c$ ?

Consider the function $f(x)=a \sin \left(\frac{x}{b}-\frac{\pi}{3}\right)-c,$ where $a>0$ and $b>0$ . If the period of $f(x)$ is $34\pi$ , the maximum value is $21$ , and $f\left(\frac{17}{6}\pi\right)=0$ , what is the value of $a+b-c$ ?

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Graphs of Trigonometric Functions - Problem Solving