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

Mathematics
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|dw:1401422933563:dw|
six trignometric functions?
yes. sin, tan, sec, cos, cot, csc

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Other answers:

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

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