Use reference triangles in an appropriate quadrant to find the...

Question

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

7. a. sec^(-1)(-√2)

Accepted Answer

Welcome back, everyone. Determine the exact value of inverse of of square root of 2. A pi divided by 2, B pi divided by 4, C 3 pi divided by 4, and D pi. Let's begin this problem by understanding that inverse of sequence. Represents an angle, so we're going to assign it to some angle theta. We want to find the value of theta, right? We can use the definition such that inverse of sequence of X is equal to inverse of cosine of 1 divided by X when the absolute value of X is greater than or equal to 1. And in this case, square root of 2 is greater than or equal to 1, so we can apply this formula, right? We can now show that theta is equal to inverse of cosine of 1 divided by square root of 2 because square root of 2 is X. And now, if we rationalize the denominator, we are going to get inverse of cosine of square root of 2 divided by 2. Let's remember the principal range. The principal range would be theta belongs to the interval from 0 to pi inclusive, excluding pi divided by 2, right? When we're considering. The values of theta equals inverse of Sean. Now, what we're going to do is simply identify the angle within this range whose cosine, right? What we can do is simply take cosine of both sides. So we're going to get cosine of theta equals square root of 2 divided by 2. So we want to find an angle theta such that cosine of theta is equal to square root of 2 divided by 2. And this is a perfect angle. Let's remember that cosine of pi divided by 4 is equal to square root of 2 divided by 2, meaning theta is pi divided by 4, which belongs to the interval. So the answer to this problem is option B. Thank you for watching.

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.7. a. sec^(-1)(-√2)

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Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.
7. a. sec^(-1)(-√2)