6csc Ø - 5 = 1
csc Ø = 6/6 = 1
then sin Ø = 1
consider the sine curve and it is clear that
Ø = π/2 or ±2π + π/2 or ±4π + π/2 ...
for the given interval, Ø = π/2
general solution:
Ø = π/2 ± 2π
no idea what all your choices mean.
-Determine a general formula (or formulas) for the solutions to the following equation. Then, determine the specific solutions (if any) on the interval [0,2pi)
-Describe in the most concise way possible the general solution to the given equation, where k is any integer. Select the correct choice below and fill in all the answer boxes within your choice.
6csctheta-5=1
a) θ=__+__k
b) θ=__+__k or θ=__+__k
c) θ=__+__k or θ=__+__k or θ=__+__k
d) θ=__+__k or θ=__+__k or θ=__+__k or θ=__+__k
2 answers
Hi Reiny, those are the choices they gave me. Apparently, I have to pick the right choice and fill it out. Below is the instruction it gave me when I filled out the wrong one.
"First, isolate the trigonometric function on one side of the equation. Next determine the quadrants in which the terminal side of the argument of the function lies or determine the axis on which the terminal side of the argument of the function lies. If the terminal side of the argument lies within a quadrant, then determine the reference angle and the value(s) of the argument on the interval [0,2π). If the terminal side of the argument of the function lies along an axis, then determine the angle associated with it on the interval [0,2π). Finally, use the period of the given function to determine the general solution.
Use the most concise way to describe the general solution by making sure that the listed equations do not produce the exact same solutions. Also, ensure that none of the general solutions that have been entered can be consolidated into a fewer number of general solutions."
"First, isolate the trigonometric function on one side of the equation. Next determine the quadrants in which the terminal side of the argument of the function lies or determine the axis on which the terminal side of the argument of the function lies. If the terminal side of the argument lies within a quadrant, then determine the reference angle and the value(s) of the argument on the interval [0,2π). If the terminal side of the argument of the function lies along an axis, then determine the angle associated with it on the interval [0,2π). Finally, use the period of the given function to determine the general solution.
Use the most concise way to describe the general solution by making sure that the listed equations do not produce the exact same solutions. Also, ensure that none of the general solutions that have been entered can be consolidated into a fewer number of general solutions."
1 answer