anonymous
  • anonymous
Find the values of the six trigonometric functions of theta: cos θ = 35/37 constraint: tan θ < 0
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1401422933563:dw|
dan815
  • dan815
six trignometric functions?
anonymous
  • anonymous
yes. sin, tan, sec, cos, cot, csc

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dan815
  • dan815
ok plug into calculator using the inverse buton
anonymous
  • anonymous
to find all six? Can you baby it down for me haha
dan815
  • dan815
okay lol
dan815
  • dan815
so first look at your triangle its 35 in x and -37 in y
dan815
  • dan815
so enter 35/-37 in your calculator, and then do cos-1 (35/-37)
dan815
  • dan815
thats a button on your calculator cos inverse
dan815
  • dan815
do the same for sin and tan
anonymous
  • anonymous
cos=2.811295299?
dan815
  • dan815
make sure you are using degree mode
anonymous
  • anonymous
ok it is now cos=161.0753556
dan815
  • dan815
that answer is in radians which is fine too if your teacher wants that
dan815
  • dan815
alright thats one, now do the rest
dan815
  • dan815
remember that 1/sin= csc 1/cos=sec 1/tan=cot
dan815
  • dan815
by the way that is not the only solution,
anonymous
  • anonymous
ya it usually accepts fractions.
dan815
  • dan815
|dw:1401423483117:dw|
dan815
  • dan815
it found that angle, but if your teacher is particular on you to only find tht last angle on the bottom
anonymous
  • anonymous
So i just plugged in -37/\[\sqrt{2594}\]
anonymous
  • anonymous
is it in quadrant 2 not 4?
dan815
  • dan815
i dont know its your choice what do you want??
anonymous
  • anonymous
well the cos is positive and the tan is negative. so wont that be quad 4?
dan815
  • dan815
yeah
anonymous
  • anonymous
ok now what would the hypotenus equal?
dan815
  • dan815
do Pythagorean thm
dan815
  • dan815
|dw:1401423730828:dw|
dan815
  • dan815
ok
anonymous
  • anonymous
i get square root of 2594
anonymous
  • anonymous
is that right? I might be doing my calcs wrong
dan815
  • dan815
looks about right
myininaya
  • myininaya
|dw:1401423880441:dw|
anonymous
  • anonymous
so would sin of theta=37/square root of 2594
dan815
  • dan815
the hypotenuse should be roughly sqrt2*36
anonymous
  • anonymous
it says it is wrong
anonymous
  • anonymous
square root of 36?
dan815
  • dan815
its -37
dan815
  • dan815
no nvm that, its just an approximation i dont have calc
myininaya
  • myininaya
cos is adj/hyp you labeled the initial triangle a bit wrong
dan815
  • dan815
okay do it over
anonymous
  • anonymous
can you show me the right triangle?
dan815
  • dan815
|dw:1401424044893:dw|
myininaya
  • myininaya
good
myininaya
  • myininaya
now find the opp measurement of the angle theta |dw:1401424168943:dw|
anonymous
  • anonymous
and how did you get that?
myininaya
  • myininaya
use the theorem we talked about last question
myininaya
  • myininaya
you are given cos is 35/37
anonymous
  • anonymous
right right right. got it
anonymous
  • anonymous
none of those are negative?
myininaya
  • myininaya
right cos is positive not negative
myininaya
  • myininaya
sin is negative
myininaya
  • myininaya
so you will definitely get a negative number for that opp measurement to theta
anonymous
  • anonymous
i got 12
myininaya
  • myininaya
and it should really be -12
anonymous
  • anonymous
35^2+b^2=37^2
anonymous
  • anonymous
b^2=144 b=12?
myininaya
  • myininaya
or b=-12 we will go with b=-12 because we were given cos is + tan is - which makes sin -
anonymous
  • anonymous
ok. so sin =-12/37
myininaya
  • myininaya
|dw:1401424409906:dw| that symbolizes the triangle is to the right of zero but below 0 (that is talking about the signs)
myininaya
  • myininaya
and yes
anonymous
  • anonymous
that clarifies completely. what about this one? tan θ is undefined. constraint: π ≤ θ ≤ 2π
anonymous
  • anonymous
find the six.
dan815
  • dan815
remember tan theta = sin theta/costheta so its undefin when cos theta= 0 which is at?
anonymous
  • anonymous
so each one would be undefined?
dan815
  • dan815
no just the tan and the cot
dan815
  • dan815
well atually no cot is fine
anonymous
  • anonymous
how do i find the rest?
dan815
  • dan815
have to first find this
dan815
  • dan815
tan theta= sin theta/cos theta => undefined when denominator =0 where cos theta =0
dan815
  • dan815
solve for cos theta = 0 , when theta is in that given interval pi to 2pi
anonymous
  • anonymous
would it be 2pi/pi?
dan815
  • dan815
no

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