Graphs of Trigonometric Functions

Sine and Cosine Graphs


The above curve is the graph of \( y=12\sin x \) with \(x > 0.\) If \(x_{1}, x_{2}, x_{3} \)and \(x_{4}\) are the \(x\)-coordinates of the intersection points of the curve and the line \(y=6,\) what is \(x_{1}+x_{2}+x_{3}+x_{4} ?\)

What is the periodicity of the function \( y=\sin2\theta ?\)

The above diagram shows a trigonometric functions with constant period \(\pi\). If \(a=3\) and \(b=1, \) what is the amplitude of the graph ?

Note: the above graph is not drawn to scale.

What is the maximum value of the function \( y= 8\sin\theta+11, \) where \(0 \leq \theta < 2\pi ?\)

Which of the following functions corresponds to the above graph?


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