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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°≈ __________

User AarCee
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2 Answers

1 vote

Answer:


\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.

User Slicekick
by
8.4k points
1 vote

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!

User Doug Knowles
by
8.5k points

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