How do you find the values of the other five trigonometric functions of the acute angle A with cscA=3?

1 Answer
Mar 21, 2018

sinA=1/3

cosA=(2sqrt2)/3

tanA=1/(2sqrt2)

cscA=3/1

secA=3/(2sqrt2)

cotA=2sqrt2/1

Explanation:

cscA=3
cscA="hypotenuse"/"opposite side"=3/1

By pythagoras theorem

"adjacent side"=sqrt(3^2-1^2)=2sqrt2

We have

"opposite side"=1
"adjacent side"=2sqrt2
"hypotenuse"=3

sinA="opposite side"/"hypotenuse"=1/3
cosA="adjacent side"/"hypotenuse"=(2sqrt2)/3
tanA="opposite side"/"adjacent side"=1/(2sqrt2)
cscA="hypotenuse"/"opposite side"=3/1
secA="hypotenuse"/"adjacent side"=3/(2sqrt2)
cotA="adjacent side"/"opposite side"=2sqrt2/1