Question

Please Help!!!! Find all solutions in the interval [0, 2π).?
1. 7 tan^3(x) - 21 tan x = 0


2. 2 sin^2(x) = sin x


3. Find all solutions to the equation. Please show your work.

cos2x + 2 cos x + 1 = 0

Answer 1

@rsnoob can u help?

Answer 2

@laura*

Answer 3

@sourwing can you please help me figure this out

Answer 4

Problem 1 use algebra to rearrange and make into a simpler function. Then graph the function and find the x-intercepts.

\[7\tan ^{3}x-21tanx=0\]
\[7\tan ^{3}x=21tanx\]
\[\tan ^{3}x=3tanx\]
\[\frac{ \tan ^{3}x }{ 3tanx }=0\]
\[\frac{ \tan ^{2}x }{ 3 }=0\]
\[\tan ^{2}x=0\]

Answer 5

You can do similar elimination of terms with the remaining equations.. For question 1 remember that the only time that tan^2 can be zero is then tanx is zero. Therefore your answer will be all places where tanx=0 on your interval (This should be a memorized graph for most Algebra II/Pre-Calc/Calc I classes).

Answer 6

but these are my choices:
pie/3 , 2pi/3, 4pi/3, 5pi/3
0, pi/5, π, 6pi/5
0, pi/3, 2pi/3, π, 4pi/3, 5pi/3
0, pi/3, π, 4pi/3

Answer 7

The Original Function Graph is attached. So evaluating by looking at the graph would be the 3rd response. (I used google to get the graph)

Answer 8

thankyou thankyou!! can you help with the others???

Answer 9

I thought it was that but i wasn't quite sure

Answer 10

2 * sin^2(x) = sin(x)
dividing both sides of equation by sin(x) gets:
(2* sin^2(x))/sin(x) = 1
dividing both sides of eqution by 2 gets:
sin^2(x)/sin(x) = 1/2
since sin^2(x) = sin(x) * sin(x), equation becomes:
(sin(x)*sin(x))/sin(x) = 1/2
which becomes:
sin(x) = 1/2
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if sin(x) = 1/2, then x = 30 degrees.
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since sin(x) = hypotenuse / y value on the graph, and since hypotenuse is always positive, and since y value on the graph is positive in quadrants 1 and 2, then sin (180-x) = sin(x).
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since 180-30 = 150, then x can be either 30 degrees or 150 degrees.

Ooops I forgot you were doing radians so just convert

Answer 11

I will help with the third if you rewrite using the double angle identity for cos and try some of the elimination steps I have shown.

Answer 12

I'm at cos^2x=-2cos-1