Half Angle Formulas: No Negative Square Roots

Thread starter armolinasf
Start date Jun 4, 2011
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Angle Formulas

In summary, half angle formulas are mathematical equations used to find the trigonometric values of angles that are half the size of a given angle. They are important because they simplify complex expressions and allow us to solve problems with difficult angles. "No negative square roots" means that the resulting values should always be positive. To use these formulas, you must know the type of angle and plug it into the formula. However, there are limitations to their use, as they only work for certain angles and may not always provide exact solutions.

Jun 4, 2011

armolinasf

Homework Statement

I'm just wondering why we don't have to worry about the possibility of taking the square root of a negative number when dealing with the half angle formulas for sine and cosine. Thanks.

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Jun 4, 2011

olivermsun

Science Advisor

What are the maximum and minimum possible values for sin x and cos x?

Jun 4, 2011

armolinasf

wow! I got it, thanks.

What are half angle formulas?

Half angle formulas are mathematical equations that are used to find the trigonometric values of angles that are half the size of a given angle.

Why are half angle formulas important?

Half angle formulas are important because they allow us to simplify complex trigonometric expressions and solve problems that involve angles that are not easily measured or calculated.

What is meant by "no negative square roots" in half angle formulas?

"No negative square roots" means that when using half angle formulas, the resulting values should always be positive. This is because negative square roots do not have real solutions.

How do you use half angle formulas to find the value of an angle?

To use half angle formulas, you first need to determine the type of angle you are working with (such as sine, cosine, or tangent). Then, plug in the given angle into the formula and solve for the half angle value.

Are there any limitations to using half angle formulas?

One limitation of using half angle formulas is that they can only be applied to certain types of angles, such as those that are multiples of 30, 45, or 60 degrees. Additionally, they may not always provide exact solutions and may require rounding to get an approximate answer.