Trigonometric ratios: csc, sec and cot
key notes :
The cotangent (cot) of an acute angle in a right triangle is a ratio. It is the length of the adjacent leg (adj) divided by the length of the opposite leg (opp). The adjacent leg is the leg next to the specified angle and the opposite leg is the side across from the specified angle.
Learn with an example
Find the cosecant of ∠G.
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
csc (G) =________
Take the formula for the cosecant of ∠G and plug in the relevant side lengths.
csc ( G ) = hyp / opp Definition of cosecant
= GI / HI Substitute hyp=GI and opp=HI
= 13 / 12 Plug in GI=13 and HI=12
So, csc (G) = 13/12 .
Find the cosecant of ∠G.
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
csc (G) = ________
Take the formula for the cosecant of ∠G and plug in the relevant side lengths.
csc (G) = hyp / opp Definition of cosecant
= FG / EF Substitute hyp=FG and opp=EF
= 53 / 45 Plug in FG=53 and EF=45
So, csc(G)= = 53 / 45 .
Find the cotangent of ∠U.
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
cot(U)= _______
Take the formula for the cotangent of ∠U and plug in the relevant side lengths.
cot(U) = adj / opp
= SU / ST Substitute adj=SU and opp=ST
= 28 / 45 Plug in SU=28 and ST=45
So, cot(U) = 28 / 45 .
let’s practice!
