Hello!
The asnwer is: Cos50° ≈ 0.643
Why?
A unit circle is a cirgle with a radius equal of 1, knowing that, also know the following:
The angle is drawn passing trough the unit circle at (0.643,0.766) it means that:
[tex]x=0.643\\y=0.766[/tex]
So,
Cos50° ≈ 0.643
We can prove that by following the next steps:
- If it's a unit circle,here is a right triangle with hypotenuse of 1,
[tex]1^{2}=x^{2}+y^{2}[/tex]
[tex]1^{2}=0.643^{2}+0.766^{2}[/tex]
[tex]1^{2}=0.4134 +0.5867[/tex]
[tex]1=1.0001=1[/tex]
- We can determine the cosine of the angle by the following formula:
[tex]cos(\alpha)=\frac{x}{hypotenuse} \\cos(\alpha)^{-1}=cos(\frac{0.643}{1})^{-1} \\\alpha=49.98[/tex]
Therefore,
Cos(α)=49.98°≈50°
Also, if there is a right triangle, according to the Pythagorean Thorem:
[tex]1^{2}=(Cos(\alpha))^{2}+(Sin(\alpha))^{2} \\Cos(50)=\sqrt{1-(Sin(50))^{2}}=0.6427[/tex]
Hence,
Cos50° ≈ 0.643
Have a nice day!
