Find all values of θ, if θ is in the interval [0°, 360°) and has ...

Question

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6.

sec θ = -√2

Accepted Answer

Hey, everyone here, we are asked to determine all possible values of theta in the interval from zero degrees to degrees, which has the same values as a given function value cos of theta is equal to the square root of two. Here we have four answer choice options. Answer choice. A theta is equal to 45 degrees, 135 degrees or degrees. Answer B theta is equal to 45 degrees or 225 degrees. Answer C theta is equal to 45 degrees or 135 degrees. And answer D theta is equal to degrees, 135 degrees or degrees. So to begin this problem, we need to recall that co sequent of theta has the equivalent ratio of R divided by Y. And now looking at our given value for sequent of theta, we can notice that this value is positive and we know that our ratio is only ever positive when we are in either the first or the second quadrants. So this tells us that we will have two values for theta one which will lie in the first quadrant and the second, which will lie in the second quadrant. So next, we need to recall that in the first quadrant, we can have coin of theta be equal to the square root of two when theta is equal to 45 degrees. So when we have coin of 45 degrees, we know that this is equal to the square root of two. And with this, we have already identified one of our values for beta as 45 degrees. And so now we need to find the other value which lies in the second quadrant. So we know coin of 45 degrees will be equal to this other value. And so to find this, we will have coin of 180 degrees. And now to be in the second quadrant, we need to subtract the 45 degrees. And now just simplifying we have coin of 135 degrees. And we know that this expression is equivalent to the square root of two. And with this, we have found our two values for theta where again, one value is in the first quadrant as 45 degrees. And the other is in the second quadrant as degrees. And with these two values we found for the, we are left with answer choice C where again, theta is equal to 45 degrees or 135 degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. sec θ = -√2