Respuesta :

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:

cosθ =  [tex]\frac{3}{5}[/tex] .

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 + [tex](\frac{4}{5}) ^{2}[/tex] = 1.

cos²θ + [tex]\frac{16}{25}[/tex] = 1.

On subtracting  [tex]\frac{16}{25}[/tex]  from both sides

cos²θ = 1 -  [tex]\frac{16}{25}[/tex] .

cos²θ =  [tex]\frac{25 -16}{25}[/tex] .

Taking square root both sides.

[tex]\sqrt{cos^{2}theta}  = \sqrt{\frac{9}{25}}[/tex] .

cosθ =  [tex]\frac{3}{5}[/tex] .

Therefore, cosθ =  [tex]\frac{3}{5}[/tex] .

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