Question

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)

Answer 1

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...

Answer 2

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

Answer 3

im i wrong?

Answer 4

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

Answer 5

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

Answer 6

Your's or mine?

Answer 7

mine. because there is a box that says x=

Answer 8

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

Answer 9

@DeoxNA erased a solution.

Answer 10

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

Answer 11

oh i see

Answer 12

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

Answer 13

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

Answer 14

Hey Asteck can I ask you another question or DeoxNa

Answer 15

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

Answer 16

@dainel40 Sure thing...

Answer 17

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

Answer 18

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

Answer 19

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?

Answer 20

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

Answer 21

The tangent of what?

Answer 22

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

Answer 23

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

Answer 24

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?

Answer 25

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

Answer 26

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...