Find the exact value of each expression. See Example 3.sin 1305°

Question

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the exact value of the sign of 1410 degrees. For our answer choices. A is the negative square root of two divided by two, B is negative by half C is the square of three divided by two and D is the negative square root of three divided by two. No, we're trying to find the exact value of our expression. But the problem is our angle, 1410 degrees doesn't fall on our unit circle. So to find its exact value, we will need to find the core terminal angle to degrees. In other words, if I draw my unit circle on the right here, and I let's say that this angle was 1410 degrees, then we are trying to find some angle that shares the same terminal side as 1410 degrees an angle that's between zero and 360 degrees for which we can easily find its exact value. So we need the least positive core terminal angle. And to find it, let's divide our value by 360 degrees, no degrees divided by degrees. When you divide them, you'll find that you get approximately 3.92. So what that tells us then that the closest value to 1410 degrees, the least positive core terminal angle will be three revolutions away. So to find it, we can subtract three multiplied by degrees from 1410. And when we do that, we get 330 degrees. So that tells us that the sign of 1410 degrees is the same value as the sign of 330 degrees. So if we know the sign of 330 degrees, we'll be able to find the sign of 1410 degrees. But we know that value, we know that the sign of 330 degrees from our unit circle equals negative half. So that means then that the sign of 1410 degrees would be equal to the same thing negative half. When we look back on our answer choices that would have been answer choice. B Thanks a lot for watching everyone. I hope this video helped.

Find the exact value of each expression. See Example 3.sin 1305°

Key Concepts

Unit Circle

Angle Reduction

Sine Function Properties

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