Lowest value that can get the sin and the cos

In summary, the lowest value that can be obtained for both "sin" and "cos" is -1, while the highest value is 1. This is defined by the Pythagorean theorem and the identities of "cos(x)" and "sin(x)" in terms of right-angled triangles. Therefore, the maximum and minimum values of "cos" and "sin" are always -1 and 1, respectively. It is important to check reliable sources, such as Wikipedia, before asking questions that may appear lazy.
  • #1
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lowest value that can get the "sin" and the "cos"

Sorry for my stupid question,but I forgot them.
What is the biggest and the lowest value that can get the "sin" and the "cos"

Thanks!
 
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  • #2
Sorry, but you should check wikipedia before posting such questions, they just show you are lazy.
 
  • #3
1.If you think of right-angled triangles, how are "cos(x)" and "sin(x)" defined in terms of the sides?
2. How can you rewrite the Pythagorean theorem in terms of a cos and sin identity?
3. What would this imply that the maxima/minima of cos and sin ought to be?
 

1. What is the lowest value that can be obtained from the sine and cosine functions?

The lowest value that can be obtained from the sine and cosine functions is -1. This occurs when the input angle is -90 degrees or -π/2 radians.

2. Can the sine and cosine functions produce values lower than -1?

No, the sine and cosine functions are limited to output values between -1 and 1. This is because they represent the ratios of the sides of a right triangle, which cannot have a length less than 0.

3. How does the lowest value of the sine and cosine functions correspond to the unit circle?

The unit circle is a circle with a radius of 1 centered at the origin. The lowest value of the sine and cosine functions (-1) corresponds to the point (-1,0) on the unit circle. This point is located at the end of the radius that forms a 270 degree angle with the positive x-axis.

4. Is the lowest value of the sine and cosine functions the same for all input angles?

No, the lowest value of the sine and cosine functions (-1) only occurs when the input angle is -90 degrees or -π/2 radians. For other input angles, the lowest value may be different.

5. How can the lowest value of the sine and cosine functions be used in real-world applications?

The lowest value of the sine and cosine functions can be used in various fields such as engineering, physics, and astronomy. For example, in physics, the lowest value (-1) represents the minimum possible displacement of an oscillating object. In astronomy, it can be used to calculate the minimum distance between two celestial bodies during their orbits.

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