Question

B=arctan(17/5) how to find all exact solutions?

Answer 1

\(\bf B = tan^{-1}\left(\cfrac{17}{5}\right)\implies tan(B) = \cfrac{17}{5}\implies \cfrac{\textit{opposite}}{\textit{adjacent}}\implies \cfrac{b}{a}\\ \quad \\
\textit{using the pythagorean theorem to find "c", we get}\\
c^2= a^2+b^2\implies c = \sqrt{a^2+b^2}\)

once you have all sides of the angle, that is, "a", "b", and "c", then you can just use that to find the trigonometric functions

Answer 2

so the exact equivalent of c is \[\sqrt{314}\]
if \[\sin =\frac{ opposite }{ hypotenuse }\]
then\[\sin \frac{ 17 }{ \sqrt{314} }=?\]

Answer 3

yeap

Answer 4

\(\bf sin(B) = \cfrac{17}{\sqrt{314}}\quad cos(B) = \cfrac{5}{\sqrt{314}}\quad csc(B) = \cfrac{\sqrt{314}}{17}\quad sec(B) =\cfrac{\sqrt{314}} {5}\)

Answer 5

anyhow got truncated. but \(\bf sec(B) =\cfrac{\sqrt{314}} {5}\)

Answer 6

thats where i get lost because my teacher is expecting an answer like:
\[\beta=\frac{ 2\pi }{ 3 }+2n \pi \] wher n is an int

Answer 7

granted that example is from \[\cos \beta=-\frac{ 1 }{ 2 }\]
i understand sin and cos just not tan

Answer 8

well.. you can always just use the arctangent function to get it.... from a calculator