Question

24) sin x = 1/3
Find cos x.

Answer 1

Answer:

$\frac{2\sqrt{2} }{3}$

Step-by-step explanation:

The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;

sin x = ( opposite / hypotenuse)

The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;

The adjacent side would be;

$\sqrt{9-1}=\sqrt{8}=2\sqrt{2}$

The cosine of an angle is given as;

cos x = (adjacent side / hypotenuse)

Therefore, the cos x would be;

$\frac{2\sqrt{2} }{3}$

Answer 2

Answer:

$cos(x) =\±2\frac{\sqrt{2}}{3}$

Step-by-step explanation:

We know that $sen(x) =\frac{1}{3}$

Remember the following trigonometric identities

$cos ^ 2(x) = 1-sin ^ 2(x)$

Use this identity to find the value of cosx.

If $sen(x) =\frac{1}{3}$ then:

$cos ^ 2(x) = 1-(\frac{1}{3})^2$

$cos ^ 2(x) =\frac{8}{9}$

$cos(x) =\±\sqrt{\frac{8}{9}}$

$cos(x) =\±2\frac{\sqrt{2}}{3}$