- #1

The_Prime_Number

- 3

- 0

-cos(60) = cos(-60) = cos(300) = cos(60)

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- Thread starter The_Prime_Number
- Start date

In summary, the trigonometric identity for cos(60) and cos(-60) is that they are both equal to 1/2. The difference between cos(60) and cos(-60) is that they have opposite signs. Cos(60) is positive while cos(-60) is negative. Cos(60) is equal to cos(-60) because they both fall on the same angle in the unit circle, but in different quadrants. The graph of cos(60) and cos(-60) are mirror images of each other across the x-axis due to the even nature of the cosine function. Understanding this identity is important in various fields for solving problems and analyzing data.

- #1

The_Prime_Number

- 3

- 0

-cos(60) = cos(-60) = cos(300) = cos(60)

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- #2

JFo

- 92

- 0

cos(-x) = cos(x) ( cos is an even function )

If you draw these angles over the unit circle, then cos(x) refers to the x component of where the ray intersects the circle. For 60 degrees and -60 degrees, the x component lies to the right of the y axis, so both are positive (and equal).

- #3

The_Prime_Number

- 3

- 0

Ok, thanks for clearing that up for me.

The trigonometric identity for cos(60) and cos(-60) is that they are both equal to 1/2.

The difference between cos(60) and cos(-60) is that they have opposite signs. Cos(60) is positive while cos(-60) is negative.

Cos(60) is equal to cos(-60) because they both fall on the same angle in the unit circle, but in different quadrants. In the first quadrant, cos(60) is positive, while in the fourth quadrant, cos(-60) is negative. Since they have the same reference angle of 60 degrees, they have the same value of 1/2.

The graph of cos(60) and cos(-60) are mirror images of each other across the x-axis. This is because the cosine function is an even function, meaning it is symmetric about the y-axis. Therefore, their values are equal but their signs are opposite.

Understanding the trigonometric identity of cos(60) and cos(-60) is important in various fields such as engineering, physics, and navigation. It helps in solving problems involving angles and trigonometric functions, and also in analyzing and interpreting data from graphs and charts.

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