Question

Let theta be an angle in quadrant III such that cos theta=-3/5 .
Find the exact values of csc theta and tan theta .

Answer 1

3-4-5- lol

Answer 2

draw a triangle. other side will be 4 by pythagoras so you have a 3 - 4 - 5 right triangle

Answer 3

quadrant III (i love the roman numerals) so sine will be negative as is cosine

Answer 4

\[\cos(\theta)=-\frac{3}{5}\] so \[\sin(\theta)=-\frac{4}{5}\]

Answer 5

cos theta =-3/5
so theta=126.86
csc 126.86=1.24
tan126.86=-1.334

Answer 6

\[\tan(\theta)=\frac{4}{3}\] the minus signs and the denominators cancel

Answer 7

\[\csc(\theta)=\frac{1}{\sin(\theta)}=-\frac{5}{4}\]

Answer 8

which, btw, is not 1.24 but rather 1.25 so forget about finding theta and using a calculator, just find the ratios

Answer 9

and in any case it is negative. you are in quadrant III so there is no way theta is 126.86. this is the danger of using a calculator with inverse trig functions so don't do it.

Answer 10

oh i guess that was all. but it should be clear than once you have cosine and know the quadrant you can find all the other trig functions yes?