Triangles AOC and BOD are congruent by SAS. Therefore, and these lengths can be found using the . Because this is the unit circle, the coordinates of points A, B, and D are equal to cosine and sine of α + β, α, and –β, respectively. Write expressions for the lengths and set them equal. Rewrite cos(-β) and sin(-β) using the identities before squaring both sides of the equation. Simplifying the resulting expressions involving cosine and sine of α, β, and α + β requires using the identity. When simplified, the equation becomes cos(α + β) = cos(α)cos(β) - sin(α)sin(β).

Adapt the speech you delivered in lesson 2 to an audience of professionals, teachers, and parents. the audience expects a more formal delivery. your listeners also expect you to use media such as images and audio to make your speech more convincing and easier to understand. your assignment should include the following elements: -at least four sources to back up your ideas -media elements to illustrate your ideas -changes to both the style and content of the speech to make it more appropriate to the audience -citations that follow mla guidelines as you revise your presentation, research and cite at least four sources. at least two of these sources must provide supporting evidence, such as charts and graphs or quotes from newspapers or other credible sources. the other two sources can provide material to grab the audience's attention — for example, photos that your audience visualize what you're talking about or music that sets the mood. you can also create original images, but these will not count as sources. here are some types of media that you may use to either show evidence or move the audience: quotes tables, charts, and graphs images video audio (including music) mix up the types of media you use so that no medium is used more than twice. take care that all your sources contribute to your speech in an obvious way. they should either back up what you're saying or make your ideas easier for your audience to understand logically or emotionally. avoid visual aids that are off topic or confusing. ask yourself these questions as you revise: am i still fulfilling the requirements of the speech i gave in lesson 2? is my speech still about a theme in franklin roosevelt's four freedoms speech? do i connect that theme to my own life and to a current issue? are my sources credible and relevant? will they convince an audience of parents, teachers, and professionals? do my media elements enhance my speech? do they set the mood, explain something difficult, or offer convincing proof? do i avoid media elements that are more distracting than ? did i cite my sources according to mla guidelines? did i check my works-cited page against sample works-cited pages to make sure it's correct?