## anonymous 3 years ago PLS HELP trig question need someone to help me

1. anonymous

2. anonymous

a.) sec(x + pi/6) = 1 1/cos(x + pi/6) = 1 cos(x + pi/6) = 1

3. anonymous

Draw the graph for cosine. Wherever cosine x = 1, so does its reciprocal, secant! -2π, 1, and 2π

4. anonymous

So, take those three numbers and subtract π/6

5. anonymous

-2π - π/6 is out of the domain, so throw that one away. The other two should be okay. I am answering fast and not checking my arithmetic, but remember that cosine and secant equal each other at the points I gave.

6. anonymous

Thanks for the medal, Gonzales

7. anonymous

one correction. when you said that the solutions for cos(0) were -2(pi), 1, and 2(pi), i think you meant 0 :)

8. anonymous

Yes -- my error! cos (0) = 1. Notice that the problem asks for sec(x+ π/6). That means (I believe) that you need to subtract π/6 from each of those points. Be careful not to go out of the domain, though (-2π to 2π).

9. anonymous

@EulersEquation just wanted to know why $2\pi-(\pi/6)$ is not in the domain will the value no be less than 2 pi

10. anonymous

2π - (π/6) = (11π)/6, which is in the domain, and is one of your answers. The other answer is 0 - π/6 = -π/6 However, -2π - (π/6) = (-13π)/6 is just outside the domain to the left.

11. anonymous

so is -pi/6 not part of the domain as well @EulersEquation

12. anonymous

13. anonymous

but how is -pi/6 in the domain @EulersEquation sorry for hassling u again and again really need help

14. anonymous

The domain is given as -2π <= x <= 2π. So, -π/6 falls within that interval. does it not?

15. anonymous

i am not sure @EulersEquation if u don't mind could u pls explaint o me how -pi/6 fall in the domain i have just started this topic and i am not very confident with it i would be really grateful if u could explain this to me.

16. anonymous

The domain is given by the interval -2π <= x <= 2π Since -π/6 is greater than -2π and is less than 2π, it falls within the given interval.

17. anonymous

oh i get it thank you @EulersEquation

18. anonymous

@EulersEquation so for the second part of the question will the answers be -pi/2 and -3pi/2

19. anonymous

The inverse of csc is sin, so you can use the sine graph. sin (-π/2) = -1, so in order for sin(x/3) = -1, x/3 = -π/2. Solving for x gives x = -3π/2. The other place in the interval where sin x = -1 is at sin(3π/2). Solving the equation x/3 = 3π/2, gives x = 9π/2, which is clearly outside the domain. So the only answer is x = -3π/2. I think (you may need to check my arithmetic).