Question

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

Answer 1

Answer:

sinθ = 5/13

Step-by-step 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:

$\sqrt{(13^2 - (-12)^2)} = opposite$

opposite = 5

Now sinθ = opposite/hypotenuse

so sinθ = 5/13