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Gonzales
 one year ago
Best ResponseYou've already chosen the best response.0a.) sec(x + pi/6) = 1 1/cos(x + pi/6) = 1 cos(x + pi/6) = 1

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2Draw the graph for cosine. Wherever cosine x = 1, so does its reciprocal, secant! 2π, 1, and 2π

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2So, take those three numbers and subtract π/6

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.22π  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.

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2Thanks for the medal, Gonzales

Gonzales
 one year ago
Best ResponseYou've already chosen the best response.0one correction. when you said that the solutions for cos(0) were 2(pi), 1, and 2(pi), i think you meant 0 :)

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2Yes  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).

u0860867
 one year ago
Best ResponseYou've already chosen the best response.0@EulersEquation just wanted to know why \[2\pi(\pi/6) \] is not in the domain will the value no be less than 2 pi

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.22π  (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.

u0860867
 one year ago
Best ResponseYou've already chosen the best response.0so is pi/6 not part of the domain as well @EulersEquation

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2It is, and is one of your answers.

u0860867
 one year ago
Best ResponseYou've already chosen the best response.0but how is pi/6 in the domain @EulersEquation sorry for hassling u again and again really need help

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2The domain is given as 2π <= x <= 2π. So, π/6 falls within that interval. does it not?

u0860867
 one year ago
Best ResponseYou've already chosen the best response.0i 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.

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2The 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.

u0860867
 one year ago
Best ResponseYou've already chosen the best response.0oh i get it thank you @EulersEquation

u0860867
 one year ago
Best ResponseYou've already chosen the best response.0@EulersEquation so for the second part of the question will the answers be pi/2 and 3pi/2

EulersEquation
 one year ago
Best ResponseYou've already chosen the best response.2The 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).
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