Give the exact value of each expression. See Example 5.csc 60°

Question

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the exact value of the trigonometric function of the count of 30 degrees. For our answer choices A is zero B is two, C is the square root of three and D is one. Now, we want to figure out the exact value of our function and we can use our special 30 60 unit triangle to help us. So let's go ahead and do that. So let's draw our triangle here and let's put our 30 degree angle at the top. Let's put in our right angle and put our 60 degree angle at the bottom. And we know that for this triangle, the base is one, the hypotenuse is two and its perpendicular height is the square root of three. Now, we also know that for this special triangle recall that the core of an angle, not necessarily 30 degrees, but generally the core of an angle is the reciprocal of its sign. So if we can find the sign of 30 degrees from our triangle, we should be able to solve for the count of 30 degrees. No, we also know that the sign of an anger equals the side that's opposite to the anger to the hypotenuse of the triangle. So four or 30 degree angle notice that our opposite side is one and the hypotenuse is two. Therefore, that tells us that the sine of 30 degrees equals the opposite side, which is one divided by the hypotenuse, which is two. Since the co equant is the reciprocal of that, that means that the core count of 30 degrees would have been the reciprocal of a half, which would have been two divided by one or simply two. Therefore, when we look at our answer choices, the co C count of 30 would have been answer choice B two. Thanks a lot for watching everyone. I hope this video helped.

Give the exact value of each expression. See Example 5.csc 60°

Key Concepts

Cosecant Function

Special Angles in Trigonometry

Unit Circle

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