6.3. Sum and Difference Identities http://www.ck12.org
6.3 Sum and Difference Identities
Here you will add six identities to your toolbox: the sum and difference identities for sine, cosine and tangent. You
will use these identities along with previous identities for proofs and simplifying expressions.
With your knowledge of special angles like the sine and cosine of 30◦and 45◦, you can find the sine and cosine of
15 ◦, the difference of 45◦and 30◦, and 75◦, the sum of 45◦and 30◦. Using what you know about the unit circle and
the sum and difference identities, how do you determine sin 15◦and sin 75◦?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61319http://www.youtube.com/watch?v=H-0jQTzfkWQ James Sousa: Sum and Difference Identities for Cosine
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61321http://www.youtube.com/watch?v=hiNDDQyee2E James Sousa: Sum and Difference Identities for Sine
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/109807http://www.youtube.com/watch?v=OQP78bwYcWw James Sousa: Sum and Difference Identities for Tangent
Guidance
There are some intuitive but incorrect formulas for sums and differences with respect to trigonometric functions. The
form below does not work for any trigonometric function and is one of the most commonincorrectguesses as to
the sum and difference identity.