Find exact values or expressions for sin A, cos A, and tan A. See...

Question

Find exact values or expressions for sin A, cos A, and tan A. See Example 1.

Accepted Answer

Hey, everyone in this problem, we're given a triangle and asked to determine expressions for sign of alpha co of alpha and 10 of alpha, we have triangle P. QR angle Q is our degree angle and angle R is going to be the angle label alpha. And so what we wanna do is write expression for sign of alpha cosine of alpha and tangent of alpha. Now, for sign of alpha recalled side of an angle is given by the opposite side divided by the hypo. So if we look at our triangle, OK. Alpha is the angle at corner R. If we look at the opposite side to this angle here, we have side R and the hypotenuse that longest side is side Q and so sign of alpha is just going to be equal to R divided by Q. All right. Now, looking at our answer choices, OK. We have four options A through D and we can already eliminate option A because it had that sign of alpha was Q divided by R. We found that it is R divided by Q. OK. So we can eliminate option ABC and D all have the correct value for sine of alpha. So we'll come back to the rest of those as we work through the rest of the problem. Now, let's move to COSA. OK. And you recall that cosine of alpha is gonna be the adjacent side divided by the hypos. So we look at her triangle or diagram, OK. The adjacent side to angle alpha is P, the hypotenuse is still Q and so codes of alpha is gonna be P divided by Q again, going back to our choices. OK. Option C and D have that cosine of alpha is equal to P divided by Q. Those are correct. Option B has the reciprocal cosine of alpha is Q divided by P that's incorrect. And so we can eliminate option B and now we're down to our last expression that we're looking for and that is gonna be 10 of alpha and we're called the tangent of an angle is going to be the opposite side divided by the adjacent side. And you know, we can also find tangent by doing sine of alpha divided by cosine of alpha. OK? Either way will work, either way will give the same answer. So if you're more comfortable with that, go ahead and do it that way, doing it. This way is just gonna avoid kind of multiplying dividing those ratios. It's gonna be a little bit more strict. And so what we have is that tangent of alpha is going to be equal to the opposite, opposite side, sorry, which is R divided by the adjacent side which is P and so we get 10 of alpha is equal to R divided by P. OK. So we have our three ratios sine of alpha is R divided by Q cosine of alpha is P divided by Q and tangent of alpha is R divided by P. Looking at our answer choices, we can see that this corresponds with answer choice D. Thanks everyone for watching. I hope this video helped see you in the next one.

Find exact values or expressions for sin A, cos A, and tan A. See Example 1.

Key Concepts

Trigonometric Ratios

Unit Circle

Reference Angles

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