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Werg22
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How to proove those formulas for any angle? So far all the proofs I've found are for angles between 0 and 2pi...
...which ones did you find?Werg22 said:How to proove those formulas for any angle? So far all the proofs I've found are for angles between 0 and 2pi...
The sine/cosine sum and difference formulas are mathematical equations that allow us to find the sine and cosine values of the sum or difference of two angles without having to calculate them separately. These formulas are used in trigonometry to simplify complex calculations and solve problems involving trigonometric functions.
The sine/cosine sum and difference formulas can be derived from the sum and difference identities of trigonometric functions. These identities state that the sine and cosine of the sum or difference of two angles can be expressed in terms of the sine and cosine of the individual angles. By rearranging these identities, we can obtain the sine/cosine sum and difference formulas.
The sine/cosine sum and difference formulas are used in various fields such as engineering, physics, and navigation. They are particularly useful in solving problems involving periodic functions, such as sound waves, light waves, and electromagnetic waves. These formulas are also used in calculating the distances and angles of objects in space.
To use the sine/cosine sum and difference formulas, you need to know the values of the individual angles. You can then substitute these values into the formulas and simplify to find the sine and cosine of the sum or difference of the angles. It is important to use the correct signs for the angles, depending on whether they are in the first, second, third, or fourth quadrant.
Yes, there are a few special cases to keep in mind when using the sine/cosine sum and difference formulas. If the angles are complementary (add up to 90 degrees), the formulas simplify to the Pythagorean identities. If the angles are supplementary (add up to 180 degrees), the formulas become negative of each other. Additionally, if the angles are equal, the formulas reduce to the double angle identities.