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.

6. b. arccsc(-2/√3)

Accepted Answer

Welcome back, everyone. Determine the exact value of inverse of co-sequence of 2 square root of 3 divided by 3. A pi divided by 3, B negative pi divided by 3, C pi divided by 6, and D negative pi divided by 6. For this problem we can essentially assign theta to inverse of cosequant of 2 square root of 3 divided by 3 because inverse of cosequant calculates a specific angle. Let's remember that inverse of cosequant. Of Y is defined as long as the absolute value of Y is greater than or equal to 1, right? And it takes values in the interval from negative divided by 2 up to pi divided by 2 inclusive, excluding 0. What we're going to do is use the reciprocal relation so we can take cosequence of both sides and we can show that cosequence of theta is equal to 2 square root of 3 divided by 3, and cosequence of theta is basically defined as 1 divided by sign of theta. So we can also solve for sign of data. Sign of theta is going to be equal to 1 multiplied by 3 divided by 2 square root of 3, right? And now we can express it as square root of 3. Divided by 2. So we know that sine of data is equal to square root of 3 divided by 2, and in that interval from negative pi divided by 2 up to pi divided by 2 excluding 0. We know that this is a perfect angle because of pi divided by 3 is equal to square root of 3 divided by 2, right, meaning the required angle theta is pi divided by 3. Which corresponds to the answer choice a. Thank you for watching.

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.6. b. arccsc(-2/√3)

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Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.
6. b. arccsc(-2/√3)