basic identities

Question

what is secΘ when the tanΘ= √3

Answer 1

Hi Grace,

tanθ = y/x or (side opposite)/(side adjacent) = √3.

So y/x = √3 or y = x√3,

Let x = 1 then y = √3,

secθ = h/x or (hypotenuse)/(side adjacent)

h = [ x² + y² ]^1/2

h = [ 1² +(√3)² ]^1/2 = 4^1/2 = 2

Therefore secθ = 2/1 = 2

You can also plug into a calculator by knowing secθ = 1/cosθ.

tanθ = √3 therefore θ = tan^-1(√3)

secθ = 1/(cos[ tan^-1(√3) ])

I hope this helps, Joe.

Answer 2

tan=opposite/adjacent

make a right triangle and find the hypotenuse because you are given the two legs

tan=√3/1

h=hypotenuse

h^2=(√3)^2+1^2

h^2=3+1

h^2=4

h=2

cos=adjacent/hypotenuse=1/2

sec=1/cos

sec is the reciprocal of the cos

therefore sec=2