Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)
sin(2x) = sin(x)

- anonymous

- katieb

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- DeoxNA

There's a pythagorean identity that says:
sin(2x)=2*sin(x)*cos(x).
so...
2cos(x)=1
cos(x)=1/2
And here's when your trig flashcards come in handy...

- anonymous

for some reason... i'm getting x = 0, pi/3/5pi/3 as the answers

- anonymous

im i wrong?

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## More answers

- DeoxNA

No, you're right, I'm wrong. Doing it graphically I do get your answers. That's odd...let me think...

- anonymous

but when i plug them in the program says I'm wrong

- DeoxNA

Your's or mine?

- anonymous

mine. because there is a box that says x=

- anonymous

NO...you get
\[x=0, \frac{ \pi }{ 3 }, \pi, \frac{ 5\pi }{ 6 }, 2\pi\]

- anonymous

@DeoxNA erased a solution.

- anonymous

by dividing \[\sin\theta\], you erase values. that's the worst mistake you can do in these questions.

- anonymous

oh i see

- anonymous

\[\sin(2x)-\sin(x)=0\]
\[2\sin(x)\cos(x)-\sin(x)=0\]
\[\sin(x)(2\cos(x)-1)=0\]

- anonymous

\[\sin(x)=0\]
or
\[\cos(x)=\frac{ 1 }{ 2 }\]

- anonymous

Hey Asteck can I ask you another question or DeoxNa

- DeoxNA

Yeah I was thinking about that, like when you get holes in the graph when you simplify rational functions...Well thank you @Azteck .

- DeoxNA

@dainel40 Sure thing...

- anonymous

Given the information below, find the exact values of the remaining circular functions of θ.
sec(θ) = 10
with θ in Quadrant IV
I got Sine= -sqrt(99)/10
Cos= 1/10
But I can't get Tangent... I tried doing Sine/Cos but I get the wrong answer

- anonymous

To get tangent... shouldnt i do sine/cos?

- DeoxNA

I'm sorry, but I don't really get what you're doing. Are you trying to convert the secant to the other circular functions? Or do you replace the secant with each respective function?

- anonymous

im just trying to get Tangent ... I already know what sine and cos are

- DeoxNA

The tangent of what?

- anonymous

- anonymous

Like I already know Sine and Cosine,.. Idk how to get Tangent

- DeoxNA

Ok, sorry I didn't get what you were saying at first....Somehow I got it this time, so if:
sec(θ)=10 in Quadrant IV
θ=4.8122
tan(4.8122)=-9.985.
How did you get an exact theta?

- anonymous

It's -√99/10.
sin^2 + cos^2 = 1
(1/10)^2 + sin^2 = 1
1/100 + sin^2 = 1
sin^2 = 99/100
sin = ± √ (99/100) = ± √99 / √100 = ± √99 / 10

- DeoxNA

Are you sure its not
(√ 99/10)/(1/10)=√ 99 ?
I know I'm not being much help, but its just that the answer makes perfect sense...

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