At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
a.) sec(x + pi/6) = 1 1/cos(x + pi/6) = 1 cos(x + pi/6) = 1
Draw the graph for cosine. Wherever cosine x = 1, so does its reciprocal, secant! -2π, 1, and 2π
So, take those three numbers and subtract π/6
-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.
Thanks for the medal, Gonzales
one correction. when you said that the solutions for cos(0) were -2(pi), 1, and 2(pi), i think you meant 0 :)
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).
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.
It is, and is one of your answers.
The domain is given as -2π <= x <= 2π. So, -π/6 falls within that interval. does it not?
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.
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.
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).