5.06 Trigonometric equations
Consider the function y = \cos \left(x - 30\right).
Sketch the graph of the function for -360 \leq x \leq 360.
Sketch the line y = \dfrac{1}{2} on the same number plane.
Hence, state all solutions to the equation \cos \left(x - 30\right) = \dfrac{1}{2} over the domain \left( - 360 , 360\right].
Consider the function y = \sin \left(x - 60\right).
Sketch the graph of the function for -360 \leq x \leq 360..
Sketch the line y = \dfrac{1}{2} on the same number plane.
Hence, state all solutions to the equation \sin \left(x - 60\right) = \dfrac{1}{2} over the domain \left[ - 360 , 360\right).
Consider the function y = 2 \sin 4 x.
Sketch the graph of the function for -120\degree \leq x \leq 120\degree.
Sketch the line y = 1 on the same number plane.
Hence, state all solutions to the equation 2 \sin 4 x = 1 over the domain \left[ - 90 \degree , 90 \degree\right]. Give your answers in degrees.
Consider the function y = 2 \sin 2 x.
Sketch the graph of the function for -180\degree \leq x \leq 180\degree.
State the other function you would add to the graph in order to solve the equation 2 \sin 2 x = 1.
Sketch the graph of this function on the same number plane.
Hence, state all solutions to the equation 2 \sin 2 x = 1 over the domain \left[ - 180 \degree , 180 \degree\right].
Consider the function y = 3 \cos 2 x + 1.
Sketch the graph of the function for -180 \leq x \leq 180.
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[ - 180 , 180\right].
Consider the function y = 2 \sin 3 x - 3.
Sketch the graph of the function for -60 \leq x \leq 60.
State the other function you would add to the graph in order to solve the equation 2 \sin 3 x - 3 = - 2.
Sketch the graph of this fuction on the same number plane.
Hence, state all solutions to the equation 2 \sin 3 x - 3 = - 2 over the domain \left[ - 120 , 120\right].
Consider the function y = - 2 \cos 3 x.
Sketch the graph of the function for -120\degree \leq x \leq 120\degree.
State the other function you would add to the graph in order to solve the equation - 2 \cos 3 x = -1.
Sketch the graph of this function on the same number plane.
Hence, state all solutions to the equation - 2 \cos 3 x = -1 over the domain \left[ - 120 \degree , 120 \degree\right].
Solve each equation for the given interval. Round your answers to one decimal place.
Consider the equation \sin \left(\dfrac{x}{2} + 60 \degree\right) = \cos \left(\dfrac{x}{2} - 60 \degree\right).
State the two functions you would graph in order to solve this equation graphically.
Sketch the graph of both of these functions using technology.
Hence, state all solutions to the equation over the domain \left[ - 360 \degree, 360 \degree\right].
Use technology to solve the following functions over the interval [0 \degree, 360 \degree). Give all solutions to the nearest degree.
Use technology to solve the following equations for 0 \leq x \leq 360. Give all solutions to two decimal places.