Question

find tan(theta) and cot(theta) if sec(theta) is 4 and sin (theta) is less than 0

Answer 1

there is a picture of an angle whose secant is \(4\) you need the other side which you find via pyathagoras
then you can take all the trig ratios you like

Answer 2

do you know another way? we're using reciprocal identities, quotient identites and pythagorean identities.

Answer 3

it is the same thing
it all amounts to finding the third side as
\[\sqrt{4^2-1^2}=\sqrt{15}\]

Answer 4

sorry if did not come back im helping some one else

Answer 5

you have
\[\sec(\theta)=4\] so right way you know
\[\cos(\theta)=\frac{1}{4}\]

Answer 6

to find the other two you need \(\sin(\theta)\) which we get from the triangle as
\[\sin(\theta)=-\frac{\sqrt{15}}{4}\] but you can use an identity if you like

Answer 7

\[\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\] if you compute
\[-\sqrt{1-\left(\frac{1}{4}\right)^2}\] you still get
\[-\frac{\sqrt{15}}{4}\] it just takes longer

Answer 8

so would i use the quotient identity cot(theta)= cos(theta)/sin(theta)?

Answer 9

yes but it is silly

Answer 10

the denominators will cancel, might as well go right to the answer you know from the triangle

Answer 11

this is the way my teacher is teaching it. first day today on this topic lol

Answer 12

you get from the triangle everything just make sure you know if it is positive or negative
\[\cot(\theta)=-\frac{1}{\sqrt{15}}\] for example

Answer 13

i sort of get it now. still trying how to find tan(theta)