Question

Consider angle θ in Quadrant ll, where cos θ= -12/13. what's the value of sin θ​

Answer 1

sinθ = 5/13

Explanation:

cosθ​ = adjacent/hypotenuse (or you could think of it as x/r)

cosθ = -12/13

adjacent = -12

hypotenuse = 13

opposite = ?

To get the opposite, we use the Pythagorean theorem

`hypotenuse^(2) = adjacent^(2) + opposite^2`

`hypotenuse^(2) - adjacent^(2) = opposite^2`

`\sqrt(hypotenuse^(2) - adjacent^(2)) = opposite`

Now sub in the numbers:

`√((13^2 - (-12)^2)) = opposite`

opposite = 5

Now sinθ = opposite/hypotenuse

so sinθ = 5/13