Half Angle Formula: Solving the Homework Statement

In summary, the half angle formula is a mathematical equation used to find the trigonometric values of half angles, derived from the double angle formula. To use it, you must identify the given angle and choose the appropriate formula for the trigonometric function. The double angle formulas are trigonometric identities used to express double angles in terms of the original angle. The half angle formula is derived from the double angle formula by dividing the double angle value by 2. Some common mistakes when using the half angle formula include not converting the angle correctly, using the wrong formula, and not simplifying the equation properly.
  • #1
tweety1234
112
0

Homework Statement



Can someone please explain how my book got [itex] sin^{2} \theta = \frac{1-cos2\theta}{2} [/itex] and [itex] cos^{2}\theta = \frac{1+cos2\theta}{2} [/itex]

As I thought the half angle formula's were [itex] sin \frac{\theta}{2} = \sqrt{\frac{1-cos\theta}{2}} [/itex]

[itex] cos\frac{\theta}{2} = \sqrt\frac{1+cos\theta}{2}} [/itex]

So how can it also be the top one's aswell?

Thanks.
 
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  • #2
Replace θ with 2θ.
 
  • #3
Doc Al said:
Replace θ with 2θ.


Oh I see, can't believe I missed that.

Thanks.
 

Related to Half Angle Formula: Solving the Homework Statement

What is the half angle formula?

The half angle formula is a mathematical equation used to find the trigonometric values of half angles. It is derived from the double angle formula and is used when the half angle is given in a problem.

How do you use the half angle formula?

To use the half angle formula, you first need to identify the given angle and whether it is in radians or degrees. Then, you can choose the appropriate formula for the trigonometric function (sine, cosine, or tangent) and plug in the half angle value. Finally, simplify the equation to find the trigonometric value of the half angle.

What are the double angle formulas?

The double angle formulas are trigonometric identities used to express the trigonometric functions of double angles in terms of the trigonometric functions of the original angle. The formulas are:
sin(2θ) = 2sinθcosθ
cos(2θ) = cos^2θ - sin^2θ
tan(2θ) = 2tanθ / 1-tan^2θ

What is the relationship between the half angle formula and the double angle formula?

The half angle formula is derived from the double angle formula by dividing the double angle value by 2. This allows us to find the trigonometric values of half angles using the double angle formula.

What are the common mistakes when using the half angle formula?

Some common mistakes when using the half angle formula include not converting the given angle to the correct form (radians or degrees), using the wrong formula for the given trigonometric function, and not simplifying the equation properly. It is important to double check your work and use the correct formula for the given problem.

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