Find the exact value of each expression. See Example 3.

sec(-495...

Question

Find the exact value of each expression. See Example 3.

sec(-495°)

Accepted Answer

Welcome back, everyone. Determine the exact value of the following trigonometric expression, and we're given sequent of negative 510 degrees. So first of all, let's notice that this angle is negative and it is very large, right? So essentially what we want to do is find its lowest positive codeterminal angle. If we're given theta of -510 degrees, we can also identify theta 1. Which is going to be a coterminal angle, right? And we are going to add 360 degrees. So first of all, we are going to take -510 degrees and then we're going to add 360 degrees. This gives us -150 degrees, so it's still negative, right? And we're going to identify our next coterminal angle. Expecting that it's going to be positive. We want, we want to get a positive value. So we're taking theta 1, which is -150 degrees, and adding 360 degrees again. And this would be 210 degrees, which is our lowest positive coterminal angle. And now this means that C count of negative 510 degrees is going to be equal to 2 of 210 degrees. And we also want to recall that scant is simply the inverse of cosine or basically the reciprocal value of cosine. So scant of 210 degrees can be expressed as one divided by cosine of 210 degrees. And now what we want to do is basically use the unit circle. Let's go ahead and do that. So we're going to take the unit circle and we're going to identify the value of 210 degrees. Let's carefully look at the circle. We start at 0 degrees. We need half of a revolution, and then in the third quadrant we have 210 degrees, right? And we also want to recall that cosine in the unit circle is represented by the X coordinate. X equals cosine of data. So now if we carefully analyze 210 degrees, we can see that it has coordinates of X equals square root of 3 divided by 2 and Y equals -12. So since we're looking for the cosine value, we're going to take the X coordinate, right? And therefore 2 of 210 degrees is going to be equal to 1 divided by the X coordinate 2 of 3 divided by 2. And now, let's take the reciprocal value. Well, we're going to get -2 divided by a square of 3, and if we rationalize it, well, we want to multiply both sides by square of 3, which is our denominator. And this gives us negative 23 divided by 3. Which is the final answer to this problem. Thank you for watching.

Find the exact value of each expression. See Example 3. sec(-495°)

Key Concepts

Secant Function

Angle Reduction

Unit Circle

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