Question

If tan=-4/3 in quadrent 2 what is cos​

Answer 1

Answer:

-3/5

Step-by-step explanation:

Answer 2

Answer:

$-\frac{3}{5}$

Step-by-step explanation:

Remember that the tangent trigonometric ratio is the opposite side of right triangle divided by the adjacent side:

$tan(\alpha )=\frac{opposite-side}{adjacent-side}$

$tan(\alpha )=-\frac{4}{3}$

Comparing the equations we can infer that:

opposite side = 4

adjacent side = 3

Now we can use Pythagoras to find the hypotenuse of our right triangle:

$hypotenuse^2=side^2+side^2$

$hypotenuse^2=4^2+3^2$

$hypotenuse^2=25$

$hypotenuse=\sqrt{25}$

$hypotenuse=5$

Remember that the cosine trigonometric ratio is the adjacent side divided by the hypotenuse; in other words:

$cos(\alpha)=\frac{adjacent-side}{hypotenuse}$

We know that adjacent side = 3 and hypotenuse = 5.

Replacing values:

$cos(\alpha )=\frac{3}{5}$

Now, remember that cosine means x and sine means y. In Quadrant 2 x is negative, which means that cosine is negative.

So, if $tan(\alpha )=-\frac{4}{3}$ in quadrant 2, then $cos(\alpha )=-\frac{3}{5}$