Let #a# be an acute angle of a right triangle for which #sec a = 13/12# Find #csc a#?
1 Answer
Apr 17, 2018
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)cosa=1/seca" and "csca=1/sina#
#•color(white)(x)sin^2a+cos^2a=1#
#rArrsina=+-sqrt(1-cos^2a)#
#"since a is acute all trig ratios are positive"#
#cosa=1/seca=1/(13/12)=12/13#
#rArrsina=sqrt(1-(12/13)^2)#
#color(white)(rArrsina)=sqrt(1-144/169)=sqrt(25/169)=5/13#
#rArrcsca=1/sina=1/(5/13)=13/5#
