Question

check all that apply. if cot theta= 3/4 and the terminal point determined by theta is in quadrant 3, then:
(a) tan theta= 4/3
(b) csc theta = -5/3
(c) sin theta= 3/5
(d) cos theta = -3/5

Answer 1

@jdoe0001 can you please help

Answer 2

\(\bf cot(\theta)=\cfrac{3}{4}\implies \cfrac{adjacent}{opposite}\implies \cfrac{a}{b}\\ \quad \\
\textit{using the pythagorean theorem }{\color{blue}{ c}}^2=a^2+b^2\implies {\color{blue}{ c}}=\pm \sqrt{a^2+b^2}\)

the pythagorean theorem doesn't tell us if the root will be negative or positive,
but we know that the angle is in
Quadrant III, that is,
cosine, or "x", is negative and
sine, or "y", is negative as well

thus we can say that \(\bf cot(\theta)=\cfrac{3}{4}\implies \cfrac{adjacent}{opposite}\implies \cfrac{a=-3}{b=-4}\)

Answer 3

once you have all sides, that is, "a", "b", and "c", then check which ones are correct from the given options, that is, which ones apply

Answer 4

I should point out that also
the pythagorean theorem doesn't tell us if the root will be negative or positive, for "c" doesn't really matter, since the radius is always positive

Answer 5

Thanks!

Answer 6

so would the answer be B and D?

Answer 7

@cwrw238

Answer 8

@jdoe0001

Answer 9

hmmm what did you for "c" anyway?

Answer 10

???

Answer 11

\(\bf cot(\theta)=\cfrac{3}{4}\implies \cfrac{adjacent}{opposite}\implies \cfrac{a}{b}\\ \quad \\
\textit{using the pythagorean theorem }{\color{blue}{ c}}^2=a^2+b^2\implies {\color{blue}{ c}}=\pm \sqrt{a^2+b^2}\)

Answer 12

keep in mind both "a" and "b" are negative

Answer 13

C = 5?

Answer 14

-5

Answer 15

yeap, so

well, is "5" since "c" is just the radius, thus is never negative

so would the answer be B and D? \(\Large \checkmark\)

Answer 16

so i was right

Answer 17

well, le'ts notice A option as well \(\bf tan(\theta)=\cfrac{b}{a}\implies \cfrac{-4}{-3}\implies \cfrac{4}{3}\)

Answer 18

so, that one applies too

Answer 19

oh ok, i should've seen that one. it's the simplest one lol :p thanks btw

Answer 20

yw

Answer 21

hmmm come to think B doesn't apply

Answer 22

what do you mean?

Answer 23

\(\bf csc(\theta)=\cfrac{c}{b}\implies \cfrac{5}{-4}\implies -\cfrac{5}{4}\)

Answer 24

oh you're right

Answer 25

@jdoe0001 can you help me with one more please

Answer 26

ok.... would be easier if you repost anew, thus more exposure anyway, and we can also revise each other

Answer 27

the answer is a and d right?

Answer 28

yes