How do you find the remaining trigonometric functions of #theta# given #costheta=sqrt3/2# and #theta# terminates in QIV?

1 Answer
Dec 1, 2017

Answer:

#"see explanation"#

Explanation:

#"since "theta" is in quadrant 4 then apart from"#

#costheta" and "sectheta" all other trig. ratios are negative"#

#•color(white)(x)costheta=sqrt3/2#

#•color(white)(x)sectheta=1/costheta=2/sqrt3=(2sqrt3)/3#

#•color(white)(x)sintheta=-sqrt(1-cos^2theta)#

#color(white)(xxxxx)=-sqrt(1-3/4)=-1/2#

#•color(white)(x)csctheta=1/sintheta=-2#

#•color(white)(x)tantheta=sintheta/costheta=-(1/2)/(sqrt3/2)=-sqrt3#

#•color(white)(x)cottheta=1/tantheta=-sqrt3/3#