hannahhaack
Find the values of the six trigonometric functions of theta: cos θ = 35/37 constraint: tan θ < 0



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hannahhaack
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dw:1401422933563:dw

dan815
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six trignometric functions?

hannahhaack
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yes. sin, tan, sec, cos, cot, csc

dan815
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ok plug into calculator using the inverse buton

hannahhaack
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to find all six? Can you baby it down for me haha

dan815
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okay lol

dan815
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so first look at your triangle its 35 in x and 37 in y

dan815
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so enter 35/37 in your calculator, and then do cos1 (35/37)

dan815
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thats a button on your calculator cos inverse

dan815
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do the same for sin and tan

hannahhaack
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cos=2.811295299?

dan815
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make sure you are using degree mode

hannahhaack
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ok it is now cos=161.0753556

dan815
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that answer is in radians which is fine too if your teacher wants that

dan815
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alright thats one, now do the rest

dan815
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remember that
1/sin= csc
1/cos=sec
1/tan=cot

dan815
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by the way that is not the only solution,

hannahhaack
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ya it usually accepts fractions.

dan815
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dw:1401423483117:dw

dan815
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it found that angle, but if your teacher is particular on you to only find tht last angle on the bottom

hannahhaack
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So i just plugged in 37/\[\sqrt{2594}\]

hannahhaack
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is it in quadrant 2 not 4?

dan815
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i dont know its your choice what do you want??

hannahhaack
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well the cos is positive and the tan is negative. so wont that be quad 4?

dan815
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yeah

hannahhaack
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ok now what would the hypotenus equal?

dan815
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do Pythagorean thm

dan815
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dw:1401423730828:dw

dan815
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ok

hannahhaack
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i get square root of 2594

hannahhaack
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is that right? I might be doing my calcs wrong

dan815
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looks about right

myininaya
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dw:1401423880441:dw

hannahhaack
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so would sin of theta=37/square root of 2594

dan815
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the hypotenuse should be roughly sqrt2*36

hannahhaack
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it says it is wrong

hannahhaack
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square root of 36?

dan815
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its 37

dan815
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no nvm that, its just an approximation i dont have calc

myininaya
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cos is adj/hyp
you labeled the initial triangle a bit wrong

dan815
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okay do it over

hannahhaack
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can you show me the right triangle?

dan815
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dw:1401424044893:dw

myininaya
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good

myininaya
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now find the opp measurement of the angle theta dw:1401424168943:dw

hannahhaack
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and how did you get that?

myininaya
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use the theorem we talked about last question

myininaya
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you are given cos is 35/37

hannahhaack
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right right right. got it

hannahhaack
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none of those are negative?

myininaya
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right cos is positive not negative

myininaya
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sin is negative

myininaya
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so you will definitely get a negative number for that opp measurement to theta

hannahhaack
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i got 12

myininaya
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and it should really be 12

hannahhaack
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35^2+b^2=37^2

hannahhaack
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b^2=144 b=12?

myininaya
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or b=12
we will go with b=12 because we were given cos is + tan is  which makes sin 

hannahhaack
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ok. so sin =12/37

myininaya
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dw:1401424409906:dw
that symbolizes the triangle is to the right of zero but below 0 (that is talking about the signs)

myininaya
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and yes

hannahhaack
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that clarifies completely. what about this one?
tan θ is undefined. constraint: π ≤ θ ≤ 2π

hannahhaack
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find the six.

dan815
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remember tan theta = sin theta/costheta
so its undefin when cos theta= 0 which is at?

hannahhaack
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so each one would be undefined?

dan815
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no just the tan and the cot

dan815
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well atually no cot is fine

hannahhaack
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how do i find the rest?

dan815
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have to first find this

dan815
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tan theta= sin theta/cos theta => undefined when denominator =0
where cos theta =0

dan815
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solve for cos theta = 0 , when theta is in that given interval pi to 2pi

hannahhaack
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would it be 2pi/pi?

dan815
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no