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Geometry

# 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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