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Sum and Difference Formulas

Sum and Difference Formulas. Often you will have the cosine of the sum or difference of two angles. We are going to use formulas for this to express in terms of products and sums of sines and cosines. The formulas are:.

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Sum and Difference Formulas

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  1. Sum and Difference Formulas

  2. Often you will have the cosine of the sum or difference of two angles. We are going to use formulas for this to express in terms of products and sums of sines and cosines. The formulas are: You will need to know these so say them in your head when you write them like this, "The cosine of the sum of 2 angles is cosine of the first, cosine of the second minus sine of the first sine of the second."

  3. Since it says exact we want to use values we know from our unit circle. 105° is not one there but can we take the sum or difference of two angles from unit circle and get 105° ? We can use the sum formula and get cosine of the first, cosine of the second minus sine of the first, sine of the second.

  4. We have a formula for sum or difference of angles for the sine function as well. The proof of this one is on page 618 in your book. The formulas are: Sum of angles for sine is, "Sine of the first, cosine of the second plus cosine of the first sine of the second." You can remember that difference is the same formula but with a negative sign.

  5. A little harder because of radians but ask, "What angles on the unit circle can I add or subtract to get negative pi over 12?" hint: 12 is the common denominator between 3 and 4.

  6. You will need to know these formulas so let's study them a minute to see the best way to memorize them. opposite cos has same trig functions in first term and in last term, but opposite signs between terms. same sin has opposite trig functions in each term but same signs between terms.

  7. There are also sum and difference formulas for tangent that come from taking the formulas for sine and dividing them by formulas for cosine and simplifying (since tangent is sine over cosine).

  8. Combined Sum and Difference Formulas

  9. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

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