SOLUTION: Draw the graph of y=cos3x-4sin x for 0°≤x<360°. Use your graph to solve the equation 3cos x-4sinx=2.5.

Algebra ->  Finance -> SOLUTION: Draw the graph of y=cos3x-4sin x for 0°≤x<360°. Use your graph to solve the equation 3cos x-4sinx=2.5.      Log On


   

Question 1199007: Draw the graph of y=cos3x-4sin x for 0°≤x<360°. Use your graph to solve the equation 3cos x-4sinx=2.5.
Answer by math_tutor2020(3838) About Me  (Show Source):
You can put this solution on YOUR website!

You can use a TI83 or TI84 calculator if you have one on hand.

Or better yet, I recommend using either Desmos or GeoGebra.
Both are faster more efficient options compared to the TI83/TI84 calculators.

Here's the Desmos link to the interactive graph
https://www.desmos.com/calculator/i2uierdtrw

Things to note about Desmos:
  • The wrench icon in the upper right corner allows you to adjust settings. Specifically we want to change radian mode into degree mode at the bottom of this settings panel.
  • The curly braces after the function tells Desmos to restrict the domain to that specific interval of 0 ≤ x < 360
  • Unfortunately there doesn't appear to be a way to change the rounding precision. It seems to be stuck at 3 decimal places. GeoGebra offers better options on this front.
The curve y = cos(3x)-4sin(x) intersects y = 2.5 at the approximate locations of
(214.509,2.5)
(298.996,2.5)
which tells us the approximate solutions to cos(3x)-4sin(x) = 2.5 are
x = 214.509
x = 298.996
This is of course when 0 ≤ x < 360
Without this domain restriction, there would be infinitely many solutions.