Question

An angle is drawn in standard position passing through the unit circle at (0.643,0.766). The angle in standard position θ has a measure of 50°.

What is cos50°?
cos50°≈ __________

Answer 1

`\text{cos}(50^(\crc))=0.643`

Explanation:

We have been given that an angle is drawn in standard position passing through the unit circle at (0.643,0.766). The angle in standard position θ has a measure of 50°. We are asked to find
`\text{cos}(50^(\crc))`.

We know that on unit circle the x-coordinates represent cos and y-coordinates represent sin.

Therefore, the value of
`\text{cos}(50^(\crc))` would be 0.643 as it represent x-coordinate of our given point.

Answer 2

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:

`x=0.643\\y=0.766`

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,

`1^(2)=x^(2)+y^(2)`

`1^(2)=0.643^(2)+0.766^(2)`

`1^(2)=0.4134 +0.5867`

`1=1.0001=1`

- We can determine the cosine of the angle by the following formula:

`cos(\alpha)=(x)/(hypotenuse) \\cos(\alpha)^(-1)=cos((0.643)/(1))^(-1) \\\alpha=49.98`

Therefore,

Cos(α)=49.98°≈50°

Also, if there is a right triangle, according to the Pythagorean Thorem:

`1^(2)=(Cos(\alpha))^(2)+(Sin(\alpha))^(2) \\Cos(50)=\sqrt{1-(Sin(50))^(2)}=0.6427`

Hence,

Cos50° ≈ 0.643

Have a nice day!