# Use double or half angle formulas

• MHB
• Elissa89
In summary, double angle formulas are mathematical equations that allow you to express trigonometric functions for angles that are twice the size of a given angle. To use them, you need to know basic trigonometric identities and specific formulas for each function. The advantages of using double angle formulas include simplifying complex expressions and solving for angles not easily found with basic functions. They are commonly used in solving trigonometric equations, simplifying expressions, and in geometry and physics. Some of the most commonly used double angle formulas include sin(2x), cos(2x), tan(2x), csc(2x), sec(2x), cot(2x), sin^2(x), cos^2(x), tan^2(x
Elissa89
Ok, So with this problem it says to use double angle or half angle formula. I have the formulas in my notes just not sure how to apply them to the problem I feel like I should be using the double formula though. Here's the problem:

cos(2*theta)+sin^2=0

Yes the double-angle formula for $\cos$ would be useful. There are a few different forms but consider that $\cos (2 \theta) = \cos^2 (\theta) - \sin^2 (\theta)$. Substituting in we get,

$\cos^2 (\theta) - \sin^2 (\theta) + \sin^2 (\theta) = \cos^2 (\theta) = 0$.

Do you have any ideas on how to solve for $\theta$?

## What are double angle formulas?

Double angle formulas are mathematical equations that allow you to express the trigonometric functions of angles that are twice the size of a given angle.

## How do you use double angle formulas?

To use double angle formulas, you need to know the basic trigonometric identities and the specific formulas for each trigonometric function. Then, you can substitute the given angle into the formula and simplify the expression.

## What are the advantages of using double angle formulas?

Using double angle formulas can make complex trigonometric expressions simpler and easier to solve. They also allow you to solve for angles that are not easily found using basic trigonometric functions.

## When should you use double angle formulas?

Double angle formulas are useful when you need to solve trigonometric equations or simplify expressions involving angles that are twice the size of a given angle. They are also helpful in finding solutions to problems in geometry and physics.

## What are the most commonly used double angle formulas?

The most commonly used double angle formulas are:
- sin(2x) = 2sin(x)cos(x)
- cos(2x) = cos^2(x) - sin^2(x)
- tan(2x) = 2tan(x) / (1-tan^2(x))
- csc(2x) = 2csc(x)cos(x)
- sec(2x) = sec^2(x) - tan^2(x)
- cot(2x) = (1 - tan^2(x)) / 2tan(x)
- sin^2(x) = (1 - cos(2x)) / 2
- cos^2(x) = (1 + cos(2x)) / 2
- tan^2(x) = (1 - cos(2x)) / (1 + cos(2x))
- csc^2(x) = (1 + cos(2x)) / sin^2(x)
- sec^2(x) = (1 + cos(2x)) / cos^2(x)
- cot^2(x) = (1 + cos(2x)) / (1 - cos(2x))

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