Find each exact function value.
csc ( ―11π/6)

Question

Find each exact function value.

csc ( ―11π/6)

Accepted Answer

Welcome back everyone. In this problem, we want to determine the exact value of the function of the core second of negative seven pi divided by four. For our answer choices A is a negative square root of two divided by two B is a negative square root of two C is negative half and D is the square root of two. No, if we're going to figure out the exact value of our function, it helps to think about what the Cosic really is. So what do we know about it? Well, recall, OK, recall that the core of an angle is actually the reciprocal of its sign. So knowing that information, then that tells us that for our function, which is the co second of negative seven pi divided by four, it's going to actually be equal to one divided by the s of negative seven pi divided by four. So this tells us then that if we can figure out the exact value of the sine of negative seven pi divided by four, then we can find its reciprocal which will be the exact value of its co second. So let's try and do that. Let's think about the sign of negative seven pi divided by four. What do we know about that expression? Well, again, recall that since the sine is an odd function that tells us then that the sine of negative seven pi divided by four is going to be equal to the negative value of the sine of seven pi divided by four. Because that's what happens when we have an odd function for an odd function, the sine of negative X equals the negative value of the sine of X. So now that we have that idea, if we can find the sine of seven fourths of pi, then we can make it negative to get the sine of negative seven pi divided by four. So how are we going to figure out that value for a sine? Well, we can use our unit circle. So using or a unit circle, let's draw our circle here. OK? And for our circle, let's put our axis oops, that's a very weird looking X axis. I think I can do better. So this is our X axis, this is our Y axis, it's our unit circle. So we have 11 negative one and a negative one. OK. Then the sign of seven fourths of pi would fall somewhere in the fourth quadrant here. OK. So let's say that that's the angle for seven fourths of pie. Now what would be the exact value here? Well, for exact value, we recall that for the unit circle, the cosine of theta is the X value. While the sine of theta is the Y value. OK. So for a circuit here, the sine of theta would be its Y value and its exact value if we recall the exact value of the sine of seven fourths of pi is actually equal to the negative square root of two divided by two. And that makes sense because we know it has to be negative because in the fourth quadrant, the Y values are negative. So that's the exact value of the sin of seven fourths of pi that tells us then that the sine of negative seven fourths of pi is going to be the negative value of that. And the negative value of negative square of two divided by two is the positive value of the square of two divided by two. No, we're almost there. Now we need to find what the kosic is. So since we know that the kosic is the reciprocal of the sine of negative seven pi divided by four, that means the core of our value is going to be reciprocal which is two divided by the square root of two. We're not done yet. All we need to do now is to is to rationalize our denominator. And we can do that by multiplying the numerator and the denominator by the square root term which is the square root of two. And if we do that two multiplied by the square of two equals two square root two and the spirit of two multiplied by the square of two equals two. Notice, we can cancel two from the numerate and denominator and that leaves us with the core second of negative seven pi divided by four being equal to the square root of two. When we look back on our answer choices that would have been answer choice. D Thanks a lot for watching everyone. I hope this video helped.

Find each exact function value.
csc ( ―11π/6)

Key Concepts

Cosecant Function

Unit Circle

Reference Angles

Watch next

Find each exact function value.csc ( ―11π/6)

Key Concepts

Cosecant Function

Unit Circle

Reference Angles

Watch next

Find each exact function value.
csc ( ―11π/6)