Question

check all that apply. If csc theta = 13/12 then:
a. tan theta = 12/5
b. sin theta = 12/13
c. cos theta = 12/13
d. sec theta = 12/13

Answer 1

\(\bf csc(\theta)=\cfrac{13}{12}\implies \cfrac{hypotenuse}{opposite}\implies \cfrac{c=13}{b=12}\\ \quad \\
\textit{using the pythagorean theorem }c^2={\color{blue}{ a}}^2+b^2\implies \sqrt{c^2-b^2}={\color{blue}{ a}}\)

once you find "a", or adjacent side, check against your choices

Answer 2

keeping in mind -> http://www.mathplanet.com/images/math/codecogs_cbc49307.gif

Answer 3

a = 25

Answer 4

how would i check?

Answer 5

a = 25?

Answer 6

I think so but how would i find out what else works?

Answer 7

\(\bf c^2={\color{blue}{ a}}^2+b^2\implies \sqrt{c^2-b^2}={\color{blue}{ a}}\implies
\sqrt{13^2-12^2}={\color{blue}{ a}}\)

you plug in your a, b and c, in the trig identities given, tangent, sine, cosine, secant
see if they match with the values for "a", "b", and "c" that you have

Answer 8

So would the answer be B, and C?

Answer 9

\(\bf \sqrt{13^2-12^2}={\color{blue}{ a}}\implies \sqrt{169-144}=a\implies \sqrt{25}=a\implies 5=a\\ \quad \\
\textit{let's test the first choice, say }tan(\theta)\\ \quad \\
tan(\theta)=\cfrac{b}{a}\implies \cfrac{13}{5}\)

there's no 1 answer
all may be correct
or some of them only
so you'd have to check all

Answer 10

hmmm dohhh I meant 12.. lemme fix that \(\bf \sqrt{13^2-12^2}={\color{blue}{ a}}\implies \sqrt{169-144}=a\implies \sqrt{25}=a\implies 5=a\\ \quad \\
\textit{let's test the first choice, say }tan(\theta)\\ \quad \\
tan(\theta)=\cfrac{b}{a}\implies \cfrac{12}{5}\)

Answer 11

so as you can see, the 1st checks out

Answer 12

Oh ok, so it would end up being A and B right

Answer 13

yeap

Answer 14

alright, thanks

Answer 15

yw