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?

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1 Answer
Apr 20, 2018

#"see explanation"#

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#