Given the right triangle below, find #cos theta#, #sin theta#, #tan theta#, #sec theta#, #csc theta#, and #cot theta#. Do not approximate, find exact answers and show all work?
1 Answer
Apr 20, 2018
Explanation:
#"to find some of the ratios we will require the third side of"#
#"the triangle"#
#"since it is right use "color(blue)"Pythagoras' theorem"#
#"third side "=sqrt(11^2-6^2)=sqrt85#
#•color(white)(x)costheta="adjacent"/"hypotenuse"=6/11#
#rArrsectheta=1/costheta=1/(6/11)=11/6#
#•color(white)(x)sintheta="opposite"/"hypotenuse"=sqrt85/11#
#rArrcsctheta=1/sintheta=1/(sqrt85/11)=11/sqrt85#
#•color(white)(x)tantheta=sintheta/costheta#
#color(white)(xxxxxx)=sqrt85/11xx11/6=sqrt85/6#
#rArrcottheta=1/tantheta=1/(sqrt85/6)=6/sqrt85#