SOLUTION: Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the sol
Algebra ->
Trigonometry-basics
-> SOLUTION: Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the sol
Log On
Question 1016305: Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.)
8 cos(theta) + 10 tan(theta) = sec(theta) Answer by ikleyn(52818) (Show Source):
You can put this solution on YOUR website! .
Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree.
Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.)
--------------------------------------------------------------------
= ,
= , <----- multiply both sides by . You will get
= , <----- replace by = ,
= ,
= .
Now introduce new variable x = for brevity. Then the last equation takes the form
= .
Solve this quadratic equation using the quadratic formula. You will get the roots
= and = .
First root doesn't fit, since it is greater than 1.
Only the root x = fits.
Thus = .
Hence, = 210° or = 330°.
Answer. = 210° or = 330°.
