Find the values in Exercises 9–12.
11. tan(arcsin(-1/2))...

Question

Find the values in Exercises 9–12.

11. tan(arcsin(-1/2))

Accepted Answer

Welcome back, everyone. Find the exact value of tangent of inverse of cosine of 1/3. A 2 square root of 2 divided by 3. B 2 square root of 2, C 2 square root of 2, and D negative 22 root of 2 divided by 3. For this problem, what we can do is simply assign theta to our angle, which is represented by inverts of cosine of 1/3. So this is where we can begin. We're going to take cosine of both sides to show that cosine of theta is equal to 1/3. Let's remember that data belongs to the interval from 0 to pi inclusive, right? And now we want to take tangent of theta. Let's remember that tangent can be expressed as the ratio between sine and cosine. We have the value of cosine. What we're going to do is identify the value of sine, and we can use the Pythagorean identity. Let's remember that sine squared of the. Plus cosine square of theta is equal to 1. So that sin of theta is equal to positive or negative, square root of 1 minus cosine square of theta. And we're going to take the positive solution because theta belongs to the interval from 0 to pi, where sine is. Non-negative, right? So what we're going to do from here is use the value of cosine. We're going to get square root of 1 minus 1/3 squared. Let's go ahead and simplify. That's square root of 1 minus 1 divided by 9, which is equal to square root of 8 divided by square root of 9. Simplifying, we're going to get a denominator of 3, and in the numerator, we're going to get 2 square root of 2. So now we have the value of sign and we are ready to identify tangent of theta. Which is simply sine divided by cosine or 2 square root of 2 divided by 3, that's the value of sine. Divided by cosine which is 1/3. We can perform division. We can simply cancel out the denominators, and this leaves us with two square root of 2, which corresponds to the answer choice B. Thank you for watching.

Find the values in Exercises 9–12.11. tan(arcsin(-1/2))

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Find the values in Exercises 9–12.
11. tan(arcsin(-1/2))