Question

Given that sin θ = sqrt(3)/7 and tan θ < 0, find sec θ and tan θ.

Answer 1

θ is in the second quad.

so you can use sin^-1 function

or you can use Pythagoras theorem and SOH CAH TOA

Answer 2

ok so

x^2 + y^2 = r^2

x^2 + sqrt(3)^2 = 7^2

x^2 + 3 = 49

x^2 = 46

x = sqrt(46)

right?

Answer 3

yes you got the adjacent right.
so now you can get the cos and the tan
but remember that both of them will be -ve

Answer 4

So

Sec θ = - 7sqrt(46)/46

Tan θ = - sqrt(138)/46

Answer 5

Yes, that's right

Answer 6

cool, thanks.

I wasn't sure if I could reduce it further.