Help with Double Angle Identities

Thread starter whittwhitt
Start date Nov 27, 2012
Tags

Angle identities

In summary, double angle identities are trigonometric equations that involve double angles. They are important because they allow us to simplify complex trigonometric expressions and solve more difficult trigonometric equations. To use double angle identities, one must know the basic trigonometric identities and substitute them into the expressions. The main difference between double angle identities and half angle identities is that the former involve double angles while the latter involve half angles. Common mistakes when using double angle identities include forgetting to use the basic identities, incorrectly substituting the double angle, and not simplifying the expression fully. It is important to carefully follow the steps and double check your work to avoid these mistakes.

Nov 27, 2012

whittwhitt

Help with Double Angle Identities!

cos θ = 24/25

The angle lies in quadrant 1; 0<θ<90

Find sin2θ

I know you would use either the formula cos^2θ - sin^2θ or 2sinθcosθ
And I know that the answer is 339/625, but I do not know how to get that answer?

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Nov 27, 2012

Simon Bridge

Science Advisor

Homework Helper

Use trig formulae and Pythagoras.
It helps if you sketch the angle in a rt-angled triangle.

Nov 28, 2012

lurflurf

Homework Helper

hint: first find sin θ

Related to Help with Double Angle Identities

1. What are double angle identities?

Double angle identities are trigonometric equations that involve double angles. They are used to simplify trigonometric expressions and solve trigonometric equations.

2. Why are double angle identities important?

Double angle identities are important because they allow us to simplify complex trigonometric expressions and solve more difficult trigonometric equations.

3. How do I use double angle identities?

To use double angle identities, you need to know the basic trigonometric identities, such as sin2x = 2sinxcosx and cos2x = cos^2x - sin^2x. Then, you can substitute the double angle identities into these basic identities to simplify the expression.

4. What is the difference between double angle identities and half angle identities?

The main difference between double angle identities and half angle identities is that double angle identities involve double angles (2x), while half angle identities involve half angles (x/2). Half angle identities are used to simplify expressions that involve half angles, while double angle identities are used to simplify expressions that involve double angles.

5. What are some common mistakes when using double angle identities?

Some common mistakes when using double angle identities include forgetting to use the basic identities, incorrectly substituting the double angle, and not simplifying the expression fully. It is important to carefully follow the steps and double check your work to avoid these mistakes.