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Sum and Difference Formulas

This lesson focuses on mastering the sum and difference formulas in trigonometry, specifically how to find the exact values of trigonometric expressions. Students will learn to split angles into known unit circle values, apply the correct formulas, and simplify results by replacing values accordingly. Using examples such as the breakdown of 75° into 30° and 45°, students will work through problems like finding cosine values and drawing corresponding triangles. Homework exercises on page 586 help reinforce these concepts.

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Sum and Difference Formulas

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  1. Sum and Difference Formulas Unit #5, Day 2 teachers.henrico.k12.va.us/.../5_4%20notes- ...

  2. Learn these!!

  3. How do we use this? Finding exact values of trig expressions • Split the given number into the sum/difference of unit circle values we know • Change the problem using the correct formula • Simplify by replacing in trig values

  4. 1. Split 75o into 30o + 45o Example: Find the exact values 2. Use the cosine formula 3. Replace with Trig values

  5. Find the exact value of 4

  6. 1. Look at your formulas. Which one does it match? Examples: Find the exact values 2. What is u and v? 3. Plug in to the left-hand side and simplify, if possible

  7. REMEMBER: Likewise,

  8. 1. Look at your cosine formula. You need to know sinv and cosu Find cos(u-v) if and 2. Draw the triangles for each given function 3. Find the missing sides 4. Find sinv and cosu 5. Put it all in your formula!

  9. Homework • Page 586 • #51, 52, 57-60, 65, 67, 68, 70-76

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