If sin θ = 3 over 7 and tan θ

Question

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

phi · Answer

I would first sketch a triangle
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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 ?

anonymous · Answer

radical 10?

phi · Answer

first simplify the equation to
x^2 + 9= 49

now add -9 to both sides

anonymous · Answer

58??

phi · Answer

49-9 = ?

phi · Answer

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

anonymous · Answer

would it be 2 radical 10?

phi · Answer

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:
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