Question

How do I do this? Please help.

Find tan θ if sec θ =sqrt(37)/6 and sin θ < 0.

Answer 1

@Darion
we will use the formula
sec^2(theta) - tan^2(theta)= 1
sec^2(theta) - 1 = tan^2(theta)
now u need to put the values given in the ques

Answer 2

so I replace theta with the value from the question?

Answer 3

yah ,in ques, value of sec(theta) is given
u need to put the value here

Answer 4

@darion any confusion?

Answer 5

So it would be sec^2(sqrt(37)/6) - 1 = tan^2(theta)?

Answer 6

nope
the formula is
sqr{sec(theta)} - 1 = sqr{tan(theta)}
u r given the value of sec(theta) = sqrt(37)/6

Answer 7

after putting the value
we get
sqr(sqrt(37)/6) - 1 = sqr{tan(theta)}
37/36-1 = sqr{tan(theta)}
1/36 = sqr{tan(theta)}
1/6 = tan(theta)

Answer 8

@darion right??????

Answer 9

Oh. I guess that makes sense. Would it be -1/6?

Answer 10

yup tan(theta) =±1/6

Answer 11

in this ques tan(theta) would be equal to -1/6
bcoz it is given sin(theta) less than 0
from this it is concluded that range of sine function is [-1,0)
as a result of this we would choose the value which should be less than 0 bcoz range of tangent function is R (real numbers)