Give the exact value of each expression. See Example 5.

cot 45°

Question

Give the exact value of each expression. See Example 5.

cot 45°

Accepted Answer

Welcome back everyone. In this problem, we want to determine the exact value of the trigonometric function of the core tangent of 30 degrees. For our answer choices A is zero B is the square root of three divided by three C is the square root of three and D is one. Now, if we're going to figure out the value of the quo tangent of 31st recall that the core tangent is equal to the reciprocal of the tangent. So the core tangent equals one divided by the tangent. So if we can figure out the tangent of 30 then we should be able to figure out what a core tangent of 30 is going to be. What do we know about the tangent of 30? Well, we can use our special triangle to help us our special 3060 triangle. And in that triangle where our angle at the top is 30 degrees, we have a right angle and the angle at the bottom is 60 degrees. Then the base of that triangle is one, its hypotenuse is two and its height is the square root of three. So we can use this triangle to help us figure out the tangent of 30 degrees because no four or 30 degree angle, we can also recall that the tangent of an angle equals the opposite side divided by the adjacent side. So it's the ratio of the opposite to the adjacent side. So that tells us then that if we can identify those sides for the 30 degree angle, we will be able to find the tangent. And thus the cotangent not four or 30 degree side, its opposite side is one and its adjacent side is the square root of three. So therefore, that tells us that the tangent of 30 degrees equals one divided by the square root of three. So since that's the tangent, that means the core tangent of 30 degrees would be equal to the reciprocal of that. That is the square root of three divided by one which equals the square root of three. When we look back on our answer choices that would have been answer choice. C Thanks a lot for watching everyone. I hope this video helped.

Give the exact value of each expression. See Example 5. cot 45°

Key Concepts

Cotangent Function

Special Angles in Trigonometry

Unit Circle

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