## dainel40 2 years ago 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)

1. 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...

2. dainel40

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

3. dainel40

im i wrong?

4. DeoxNA

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

5. dainel40

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

6. DeoxNA

Your's or mine?

7. dainel40

mine. because there is a box that says x=

8. Azteck

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

9. Azteck

@DeoxNA erased a solution.

10. Azteck

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

11. dainel40

oh i see

12. Azteck

$\sin(2x)-\sin(x)=0$ $2\sin(x)\cos(x)-\sin(x)=0$ $\sin(x)(2\cos(x)-1)=0$

13. Azteck

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

14. dainel40

Hey Asteck can I ask you another question or DeoxNa

15. DeoxNA

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

16. DeoxNA

@dainel40 Sure thing...

17. dainel40

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

18. dainel40

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

19. 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?

20. dainel40

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

21. DeoxNA

The tangent of what?

22. dainel40

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

23. dainel40

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

24. 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?

25. dainel40

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

26. 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...