Concept Check Work each problem. Without using a calculator, d...

Question

Concept Check Work each problem. Without using a calculator, determine which of the following numbers is closest to sin 115°: -0.9, -0.1, 0, 0.1, or 0.9.

Accepted Answer

Welcome back, everyone in this problem, we want to write the number which is closest to the value of the cosine of 123 degrees. For our answer choices A is negative one B is negative 0.5 C is 0.5 and D is one. Now, we're doing a bit of estimation here, we want the number that's closest to the value of the cosine of 123 degrees. So first, we need to figure out where the cosine of 123 degrees is before we can estimate. And the best thing to help us is by using the unit circle. So let's go ahead and do that. OK. Let me draw the unit circle on the, on the right here. OK. And on our unit circle, 123 degrees would be somewhere in the second quadrant. Let's call it somewhere about there, right? No, that's pretty important because recall that on the unit circle, on the unit circle, each chord in it is written in the form of the cosine of theater and the sign of theater where the cosine of theater is the X value and the sign of theater is the Y value. So since the cosine of theta is the X value and the cosine of 123 is in the second quadrant, we know that in the second quadrant, the X value is negative. So that tells us then that, so that tells us that the core sign of 123 degrees would also be negative. So that means it couldn't be, one, couldn't be 0.5. Now, what else do we know? But we know that we're working with the unit circle. So the X values range from negative 1 to 1 and a negative one or angle would be 180 degrees. So we know that the cosine of 180 degrees equals negative one. Is there anything else we know about any other angles in the second quadrant? Well, we also know that the core sign of 120 degrees equals negative a half. OK? The cosine of 120 degrees equals negative a half or that's negative 0.5. So the question is which one is the core sign of 123 degrees closer to, well, 120 is closer to 123 compared to 180. So that tells us then that the core sign of 123 degrees is closer to the core sign of 100 and 20 degrees, which is equal to negative 0.5 when we look back in our answer choices that would have been answer choice. B thanks a lot for watching everyone. I hope this video helps.

Concept Check Work each problem. Without using a calculator, determine which of the following numbers is closest to sin 115°: -0.9, -0.1, 0, 0.1, or 0.9.

Key Concepts

Unit Circle and Angle Measurement

Sine Function Properties in Different Quadrants

Reference Angles and Approximation

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