Question

If sinθ =4/5 , then cosθ = _____.

Answer 1

Cosθ is 3/5 because the cosine is found from the adjacent side of the triangle being divided by the hypotenuse. The sine is found by putting the opposite side from θ over the hypotenuse. If you draw this triangle out, the side across from θ would be 4 and the hypotenuse 5. In order to find the opposite side, you could either solve with the pythagorean theorem (a^2+b^2= c^2) or you could remember the properties of a triangle, therefore the final side is 3. You then put the opposite, 3, over the hypotenuse,5, in order to get 3/5 for the cosθ.

Answer 2

Answer:

cosθ =  $\frac{3}{5}$ .

Step-by-step explanation:

Given : If sinθ =4/5 .

To find :  cosθ = _____.

Solution : We have given that sinθ =4/5 .

By the trigonometric identity

cos²θ + sin²θ = 1.

Plugging the value of sinθ =4/5 .

cos²θ + $(\frac{4}{5}) ^{2}$ = 1.

cos²θ + $\frac{16}{25}$ = 1.

On subtracting  $\frac{16}{25}$  from both sides

cos²θ = 1 -  $\frac{16}{25}$ .

cos²θ =  $\frac{25 -16}{25}$ .

Taking square root both sides.

$\sqrt{cos^{2}theta} = \sqrt{\frac{9}{25}}$ .

cosθ =  $\frac{3}{5}$ .

Therefore, cosθ =  $\frac{3}{5}$ .