Question

If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ?

Answer 1

I would first sketch a triangle

sin is opposite over hypotenuse
so 3/7 means opposite side is 3 and hypotenuse is 7
what is the "x" side ?

we would use pythagoras to find x
x^2 + y^2 = h^2
x^2 + 3^2 = 7^2
can you find x ?

Answer 2

radical 10?

Answer 3

first simplify the equation to
x^2 + 9= 49

now add -9 to both sides

Answer 4

58??

Answer 5

49-9 = ?

Answer 6

you get
x^2 = 40
now take the square root of both sides

Answer 7

would it be 2 radical 10?

Answer 8

once we know x, we can find cos
however, the angle could be in any of 4 quadrants.

but we know the sin is 3/7 is positive.
the hypotenuse is always positive.
but we would also have these: