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

Question

Accepted Answer

Hello, today we're going to be determining the exact value of the given trigonometric function. So we want to identify the value of C of 30 degrees. Now, in order to answer this problem, we're going to need the help of a unit circle. So let's go ahead and first identify the location of our given angle inside of the trigger metric value. We are given the angle of 30 degrees. So let's go ahead and identify where 30 degrees is located on the unit circle. 30 degrees can be found in the first quadrant of the unit circle. And the corresponding terminal point to this angle is the square root three divided by two comma one divided by two. Now recall that every terminal point on the unit circle is identified as cosine comma s sign. What this means is that cosine represents every X value on the terminal points and sine represents every Y value on the terminal points. But notice that terminal points are not identified with any seeking values. So how can we find seeking of 30 degrees? Well, recall that the identity for seeking data is equal to the inverse of cosine theta. So what this means is that if we want to identify seeking data or seeking of degrees, we're going to need the value of cosine of 30 degrees. So let's first start by identifying cosine of 30 degrees. Well, again, cosine is every X value on the terminal points. So we just need to pay attention to the X value for the terminal point of 30 degrees. That X value in this point is going to be square over three divided by two. So that means that cosine of 30 degrees is equal to the square root of three divided by two. Now that we have the cosine value, we can use this value to help us find sein of degrees. And again, seeking is going to be the inverse of the cosine value. So if cosine is equal to the square root three divided by two, then seeking will equal to the inverse which will be two divided by the square root of three. Now, in this case here, we have a square root in the denominator. So we're going to need to rationalize the denominator in order to do this, we're going to multiply the numerator and the denominator by the square root of three. Doing this will allow us to rewrite seeking of 30 degrees as two multiplied by the square root of three divided by three. And this will be the value of the given trigonometric function. And with that being said, the answer to this problem is going to be b 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.sec 45°

Key Concepts

Secant Function

Special Angles in Trigonometry

Unit Circle

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