SOLUTION: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
2 sin^2 x + 7 cos x = 5
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Question 1118055: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
2 sin^2 x + 7 cos x = 5
sec^2 x − 3 tan x = −1
tan^2 x + tan x − 30 = 0
Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use n as an integer constant.)
y = sin πx/8+1
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
2 cos x/3-sqrt2=0
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ +\ 7\cos(x)\ =\ 5)
\)\ +\ 7\cos(x)\ -\ 5\ =\ 0)
\ -\ 7\cos(x)\ +\ 3\ =\ 0)
Let )
(u\ -\ 3))
Substitute back
\ =\ \frac{1}{2})
But \ \leq\ 1)
, so discard \ =\ 3)
\ =\ \frac{\pi}{3})
Or
\ =\ \frac{5\pi}{3})
John
My calculator said it, I believe it, that settles it
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
2 sin^2 x + 7 cos x = 5
2(1-cos^2(x)) + 7cos(x) = 5
2-2cos^2(x) + 7cos(x) = 5
2cos^2(x) - 7cos(x) + 3 = 0
(2cos(x)-1)(cos(x)-3) = 0
cos(x) = 1/2 or cos(x) = 3 (extraneous)
Ans: x = pi/3 or x = -pi/3
---------------------------------
sec^2 x − 3 tan x = −1
tan^2(x)+1 - 3tan(x) = -1
tan^2(x) - 3tan(x) +2 = 0
(tan(x)-1)(tan(x)-2) = 0
tan(x) = 1 or tan(x) = 2
x = pi/4 or 5pi/4 or 1.107 or 4.25
----------------------------------
tan^2 x + tan x − 30 = 0
(tan(x)+6)(tan(x)-5) = 0
tan(x) = -6 or tan(x) = 5
x = -1.406 or -4.547 or 1.373 or 4.515
Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use n as an integer
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
2 cos x/3-sqrt2=0
2*cos(x/3) = sqrt(2)
cos(x/3) = sqrt(2)/2
x/3 = arccos(sqrt(2)/2) = 0.7854 or -0.7854
x = 2.356 or -2.356
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Cheers,
Stan H.
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