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anonymous
 one year ago
ALGEBRA 2/TRIG HELP PLEASE PLEASE HELP
anonymous
 one year ago
ALGEBRA 2/TRIG HELP PLEASE PLEASE HELP

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @pooja195

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437061318167:dwOk, first thing you need to do is find what the hypotenuse is. It's a right triangle, so can use the Pythagorean Theorem to figure out what the (?) on the drawing is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Close! The hypotenuse is \(\sqrt{13}\) since the hypotenuse squared is 13.dw:1437061696572:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay :) what do I need to do next?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, now, we need to remember what sine, cosine, and tangent represent on a right triangle. The mnemonic device is SOH CAH TOA. S=Sine C=Cosine T=Tangent O=Opposite A=Adjacent H=Hypotenuse So, for example: \[\sin(\theta)=\frac{\text{side opposite of }\theta}{\text{hypotenuse}}\]The other 2, cosine and tangent work the same way in the mnemonic device. So, can you tell me what sine would be using this triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sine would be 3/13, right? Which would make it 0.23076923076

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait, I forgot to square 13

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember, the hypotenuse is \(\sqrt{13}\), so \(\sin(\theta)=\frac{3}{\sqrt{13}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be 0.83205029433

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nice. Using the mnemonic SOH CAH TOA, you can figure out what cosine and tangent represent. \[\cos(\theta)=\frac{\text{side adjacent to }\theta}{\text{hypotenuse}}\]\[\tan(\theta)=\frac{\text{side opposite to }\theta}{\text{side adjacent to }\theta}\]Can you figure out the rest?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cosine would be 2/√13=0.55470019622 and tangent would be 3/2=1.5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Good job. I'd recommend for future reference, I'd just get it into your head that sine, cosine, and tangent are those ratios right there. It'll make your life easier as you go further into trig.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much!! :) You were a great help.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Also, it didn't happen in this question, but remember, negatives stick with the calculation! So, if the point were in quadrant II (so the point would be (2, 3)), then the xvalue would be 2!! So, if you were given that, \(\sin(\theta)=\frac{3}{\sqrt{13}}\), \(\cos(\theta)=\frac{2}{\sqrt{13}}\), and \(\tan(\theta)=\frac{3}{2}\). See how the negative carried over?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's a good tip to remember; I almost always forget to carry the negative sign
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