## dainel40 Group Title 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) one year ago one year ago

1. DeoxNA Group Title

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 Group Title

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

3. dainel40 Group Title

im i wrong?

4. DeoxNA Group Title

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

5. dainel40 Group Title

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

6. DeoxNA Group Title

Your's or mine?

7. dainel40 Group Title

mine. because there is a box that says x=

8. Azteck Group Title

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

9. Azteck Group Title

@DeoxNA erased a solution.

10. Azteck Group Title

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

11. dainel40 Group Title

oh i see

12. Azteck Group Title

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

13. Azteck Group Title

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

14. dainel40 Group Title

Hey Asteck can I ask you another question or DeoxNa

15. DeoxNA Group Title

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 Group Title

@dainel40 Sure thing...

17. dainel40 Group Title

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 Group Title

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

19. DeoxNA Group Title

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 Group Title

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

21. DeoxNA Group Title

The tangent of what?

22. dainel40 Group Title

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 Group Title

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

24. DeoxNA Group Title

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 Group Title

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 Group Title

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...