Give the exact value of each expression. See Example 5. tan 30...

Question

Give the exact value of each expression. See Example 5. tan 30°

Accepted Answer

Hello, today we're going to be determining the value of the given trigonometric function. So we are asked to determine the value of tangent of degrees. In order to answer this question, we're going to need the help of a unit circle. So in order to approach this problem, let's first identify where the angle 60 degrees lies on the unit circle. The angle 60 degrees can be found in the first region of the unit circle. And the terminal point given to us at this angle is one divided by two comma square root three divided by two. Now recall that any terminal point that lies on the unit circle is defined as cosine comma S sign. This is where cosine represents every X value of the terminal points and sine represents every Y value of the terminal points. But notice that the terminal points do not involve tangent in the ordered pairs. So how can we determine tangent of 60 degrees using the given terminal point at 60 degrees on the unit circle will recall that the identity for tangent of data is equal to the Y value divided by the X value at the terminal point of 60 degrees. The Y value is given to us as the square root three divided by two. And the X value is given to us as one divided by two. So what we can go ahead and do is we can set up the division between these two values. We're going to take the square root three divided by two and divide this value by one divided by two. And now, what we'll need to do is we need to simplify this complex fraction. In order to simplify this complex fraction, we're going to multiply the denominator by its reciprocal two divided by one. And since we are multiplying the denominators reciprocal, we're also going to have to multiply the reciprocal to the numerator as well. This will allow us to reduce the denominator to one. And that leaves us with the square root three divided by two, multiplied by two, divided by one. Using cross elimination, we can reduce both of the twos to one. And what we are left with is the square root of three multiplied by one, which will give us a final value of the square root of three. So what this means is that the value of tangent of 60 degrees is equal to the square root of three. And with that being said, the answer to this problem is going to be c So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Give the exact value of each expression. See Example 5. tan 30°

Key Concepts

Definition of the Tangent Function

Special Angles and Their Exact Values

Using the 30°-60°-90° Triangle

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