Graphs of Trigonometric Functions

Sine and Cosine Graphs


The above curve is the graph of y=12sinx y=12\sin x with x>0.x > 0. If x1,x2,x3x_{1}, x_{2}, x_{3} and x4x_{4} are the xx-coordinates of the intersection points of the curve and the line y=6,y=6, what is x1+x2+x3+x4?x_{1}+x_{2}+x_{3}+x_{4} ?

What is the periodicity of the function y=sin2θ? y=\sin2\theta ?

The above diagram shows a trigonometric functions with constant period π\pi. If a=3a=3 and b=1,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=8sinθ+11, y= 8\sin\theta+11, where 0θ<2π?0 \leq \theta < 2\pi ?

Which of the following functions corresponds to the above graph?


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