Consider the function y = 3 \sin x and the line y = 3 which are graphed below:
State all solutions to the equation 3 \sin x = 3 over the domain \left[ - 2 \pi , 2 \pi\right].
Graph the function y = \tan x and the line y = 1 on the same number plane over the domain \left[ - 2 \pi , 2 \pi\right].
Hence, state all solutions to the equation \tan x = 1 over the domain \left[ - 2 \pi , 2 \pi\right].
Consider the graph of y = \cos x over the domain [0, 2 \pi ]:
State the x-values for which \cos x = 0.
State the first x-value for which \cos x = 0.5
For what other value of x shown on the graph, does \cos x = 0.5?
For what values of x does \cos x = - 0.5?
Consider the graph of y = \tan x:
How long is one period of the graph?
State the x-values for which \tan x = 0, from x = 0 to x = 2 \pi inclusive.
State the first x-value for which \tan x = 1.
For what other value of x shown on the graph does \tan x = 1?
For what values of x shown on the graph does \tan x = - 1?
Consider the function y = \cos \left(\dfrac{x}{4}\right).
Sketch the graph of this function over the domain [-4 \pi, 4\pi].
Sketch the line y = - 0.5 on the same number plane.
Hence, state all solutions to the equation \cos \left(\dfrac{x}{4}\right) = - 0.5 over the domain \left[ - 4 \pi , 4 \pi\right] in exact form.
Consider the function y = \tan \left(x - \dfrac{\pi}{4}\right).
Sketch the graph of the function for -2\pi \leq x \leq 2\pi.
Sketch the line y = 1 on the same number plane.
Hence, state all solutions to the equation \tan \left(x - \dfrac{\pi}{4}\right) = 1 over the domain \left[ - 2 \pi , 2 \pi\right). Give your answers as exact values.
Consider the function y = 3 \cos 2 x + 1.
Sketch the graph of the function for -\pi \leq x \leq \pi.
State the other function you would add to the graph in order to solve the equation 3 \cos 2 x + 1 = \dfrac{5}{2}.
Sketch the graph of this function on the same number plane.
Hence, state all solutions to the equation 3 \cos 2 x + 1 = \dfrac{5}{2} over the domain \left[ - \pi , \pi\right]. Give your answers as exact values.
Consider the function y = \sin \left(x - \dfrac{\pi}{3}\right) + 5.
Sketch the function y = \sin \left(x - \dfrac{\pi}{3}\right) + 5 over the domain [- 2 \pi, 2 \pi].
Sketch the line y = \dfrac{11}{2} on your graph.
Hence, state all solutions to the equation \sin \left(x - \dfrac{\pi}{3}\right) + 5 = \dfrac{11}{2} over the domain \left[ - 2 \pi , 2 \pi\right). Give your answers in exact form.
Consider the equation 3 \sin \left( 3 x + \dfrac{\pi}{7}\right) = - \dfrac{11}{10}.
Which function would be graphed along with y = - \dfrac{11}{10} in order to solve the equation graphically?
Graph both of these functions using the graphing facility of your calculator. Hence state all solutions to the equation over the domain \left[ - \dfrac{13\pi}{42}, \dfrac{5\pi}{14}\right]. Round your answers correct to three decimal places.
Consider the equation - 5 \cos \left(\dfrac{x}{2} + \dfrac{\pi}{5}\right) = - \dfrac{17}{10}.
Which function would be graphed along with y = - \dfrac{17}{10} in order to solve the equation graphically?
Graph both of these functions using the graphing facility of your calculator. Hence state all solutions to the equation over the domain \left[ - \dfrac{7 \pi}{5} , \dfrac{13 \pi}{5}\right]. Round your answers correct to three decimal places.
Determine the equation of the graphed function given that it is of the form y = \cos \left(x - c\right), where c is the least positive value.
Determine the equation of the graphed function given that it is of the form y = \sin \left(x - c\right), where c is the least positive value.
Determine the equation of the graphed function given that it is of the form \\ y = \sin \left(x + c\right) + d, where c is the least positive value and x is in radians.
Determine the equation of the graphed function given that it is of the form y = a \cos \left(x - c\right), where c is the least positive value and x is in radians.
Determine the equation of the graphed function given that it is of the form \\ y = - \sin \left(x - c\right) - d, where c is the least positive value and x is in radians.
Determine the equation of the graphed function given that it is of the form \\ y = - \cos \left(x + c\right) - d, where c is the least positive value and x is in radians.