Question

Find the other dive trigonometric functions OF the acute angle A, given that sec A=2 ?

Answer 1

Given,secA = 2.
So, cosA = 1/2 = cos 60.
Then, A = 60 degree.
Now, Sin 60 = `(sqrt 3)/2`,tan 60 = `sqrt 3`, csc 60 = `2/(sqrt3)`, cot 60 =`1/(sqrt3)`.

ANOTHER WAY
We know, secA =`2/1= (hypotenuse)/(base)`
So, height = `sqrt[(hypotenuse)^2-(base)^2]`
So, height = `sqrt[2^2-1^2]`
`rArr sqrt3`

Answer 2

Given,secA = 2.
So, cosA = 1/2 = cos 60.
Then, A = 60 degree.
Now, Sin 60 = `(sqrt 3)/2`,tan 60 = `sqrt 3`, csc 60 = `2/(sqrt3)`, cot 60 =`1/(sqrt3)`.

ANOTHER WAY
We know, secA =`2/1= (hypotenuse)/(base)`
So, height = `sqrt[(hypotenuse)^2-(base)^2]`
So, height = `sqrt[2^2-1^2]`
`rArr sqrt3`
Now sinA =`(height)/(hypotenuse)=sqrt3/2`
CosA= `(base)/(hypotenuse)=1/2`,
TanA = `(height)/(base)=(sqrt3)/1`
CscA = 1/sinA =`1/[(sqrt3)/2]= 2/(sqrt3)`,
CotA= 1/tanA =`1/(sqrt3)`