Understanding Cosine: How to Find the Value of Cosine 30 Degrees Using the Unit Circle and Trigonometric Identities

cos 30°

To find the value of cosine 30 degrees, we need to use the unit circle or trigonometric identities

To find the value of cosine 30 degrees, we need to use the unit circle or trigonometric identities.

First, let’s use the unit circle. The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of a coordinate plane. To find the cosine of an angle, we look at the x-coordinate of the point where the angle intersects the unit circle.

For 30 degrees, we need to find the point on the unit circle that corresponds to 30 degrees. Since 30 degrees is a reference angle in the first quadrant, the x-coordinate of the point is the cosine of 30 degrees.

Next, let’s use the trigonometric identity. The cosine of an angle can also be found using the following identity: cos θ = cos(90° – θ).

Since 30 degrees is less than 90 degrees, we can use this identity to find the cosine of 30 degrees as follows:

cos 30° = cos(90° – 30°)
= cos 60°

Now, we need to find the value of the cosine of 60 degrees. Again, we can use the unit circle or the trigonometric identity.

On the unit circle, the angle 60 degrees corresponds to the (1/2, √3/2) point, where the x-coordinate is 1/2. Therefore, cos 60° = 1/2.

Alternatively, we can also use the trigonometric identity cos θ = cos(90° – θ):

cos 60° = cos(90° – 60°)
= cos 30°

So, we have cos 30° = cos 60° = 1/2.

Therefore, the value of cos 30° is 1/2.

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