Derive Cosine of a Sum Identity
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Lesson Summary:
This lesson teaches how to derive the formula for the cosine of the sum of two angles using the unit circle definition of sine and cosine, the Pythagorean identity, and the distance formula. The video also highlights the importance of knowing that the cosine of a plus b is not equal to the cosine of a plus the cosine of b. By the end of the lesson, students will have learned how to derive the formula for the cosine of the sum of two angles and apply it to compute angles like the cosine of 60 degrees plus 45 degrees.
Lesson Description:
This video shows the formula for deriving the cosine of a sum of two angles.
More free YouTube videos by Julie Harland are organized at http://yourmathgal.com
Questions answered by this video:
- What is cos(A + B)?
- What is the formula for cos(A + B)?
- How can you derive the formula for the cosine of the sum of two angles using unit circle definitions, the pythagorean identity, and the distance formula?
- Why does cos(A + B) = cosA*cosB - sinA*sinB?
- What is the distance formula between two points?
- What is the pythagorean trig identity?
- Why does cos(A + B) not equal cosA + cosB?
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Staff Review
This lesson will teach you about the cosine of the sum of two angles. You will also learn why the formula for breaking apart the cosine of the sum of two angles works. The proof of this identity is explained and proved in this video. All steps involved in the proof are explained and shown very clearly. The algebra done can get a little complicated, but it is very complete.
