14-4 Sum and Difference Identities Check it out

14-4 Sum and Difference Identities Check it out

14-4 Sum and Difference Identities Check it out Does the sin(75) =sin(45)+sin(30) ? Holt Algebra 2 14-4 Sum and Difference Identities Holt Algebra 2 14-4 Sum and Difference Identities Example 1A: Evaluating Expressions with Sum and Difference Identities Find the exact value of cos 15. Write 15 as the difference 45 30 because

cos 15 = cos (45 30) trigonometric values of 45 and 30 are known. Apply the identity for cos (A B). = cos 45 cos 30 + sin 45 sin 30 Evaluate. Simplify. Holt Algebra 2 14-4 Sum and Difference Identities Example 1B: Proving Evaluating Expressions with Sum and Difference Identities Find the exact value of . Write

as the sum of Apply the identity for tan (A + B). Holt Algebra 2 14-4 Sum and Difference Identities Example 1B Continued Evaluate. Simplify. Holt Algebra 2 14-4 Sum and Difference Identities

Check It Out! Example 2 Prove the identity . Apply the identity for cos A + B. Evaluate. = sin x Holt Algebra 2 Simplify. 14-4 Sum and Difference Identities Check It Out! Example 1b Find the exact value of each expression.

Write as the sum of because trigonometric values of and are known. Apply the identity for sin (A B). Holt Algebra 2 14-4 Sum and Difference Identities Check It Out! Example 1b Continued Find the exact value of each expression. Evaluate.

Simplify. Holt Algebra 2 14-4 Sum and Difference Identities Example 3: Using the Pythagorean Theorem with Sum and Difference Identities Find cos (A B) if sin A = if tan B = with 0 < A < and with 0 < B < Step 1 Find cos A, cos B, and sin B.

Use reference angles and the ratio definitions sin A = and tan B = Draw a triangle in the appropriate quadrant and label x, y, and r for each angle. Holt Algebra 2 14-4 Sum and Difference Identities Example 3 Continued In Quadrant l (Ql), 0 < A < 90 and sin A = . r=3 A x

Holt Algebra 2 In Quadrant l (Ql), 0< B < 90 and tan B = . r y=1 B x=4 y=3 14-4 Sum and Difference Identities Example 3 Continued r=3 A

r y=3 y=1 x B x=4 x2 + 12 = 32 32 + 42 = r2 Thus, cos A = and sin A = Holt Algebra 2

Thus, cos B = sin B = . and 14-4 Sum and Difference Identities Example 3 Continued Step 2 Use the angle-difference identity to find cos (A B). cos (A B) = cosAcosB + sinA sinB Apply the identity for cos (A B). Substitute

for cos A, for cos B, and cos(A B) = Holt Algebra 2 Simplify. for sin B. 14-4 Sum and Difference Identities Check It Out! Example 3 Find sin (A B) if sinA = with 90 < A < 180 and if cosB = with 0 < B < 90. In Quadrant ll (Ql), 90< A < 180 and

sin A = . In Quadrant l (Ql), 0< B < 90 and cos B = r=5 y=4 A x Holt Algebra 2 y r=5 B

x=3 14-4 Sum and Difference Identities Check It Out! Example 3 Continued r=5 y=4 y r=5 A x B x=3 x2 + 42 = 52

52 32 = y2 Thus, sin A = Thus, cos B = and cos A = sin B = Holt Algebra 2 and 14-4 Sum and Difference Identities Check It Out! Example 3 Continued

Step 2 Use the angle-difference identity to find sin (A B). sin (A B) = sinAcosB cosAsinB Apply the identity for sin (A B). Substitute for sin A and sin B, for cos A, and for cos B. sin(A B) = Holt Algebra 2 Simplify. 14-4 Sum and Difference Identities

Lesson Quiz: Part I 1. Find the exact value of cos 75 2. Prove the identity sin 3. Find tan (A B) for sin A = cos B = with 0

Recently Viewed Presentations

  • Nanomedicine

    Nanomedicine

    Nanotechnology is the study of particles 1x10 ^-9 of a meter in size. Over the past decade the field has gained tremendous ground, including nanomedicine. Nanomedicine is the application of nanotechnology to do everything from precise delivery of drugs to...
  • Personal protective equipment (PPE)

    Personal protective equipment (PPE)

    Workers exposed to noise at or above 85 dBA for 8-hour TWA shall participate in an annual training program. ... Electrical panels, any equipment that has to be energized to perform service/maintenance work. Other Considerations.
  • Celebrate the Harvest

    Celebrate the Harvest

    Help students with reading skills at OSFC. Food & Care Coalition. Meals on Wheels. Habitat for Humanity. Daughter of Utah Pioneers Museum. Music and Theater. Utah Valley Symphony. Hale Center Theater. ... Day Trips. Longer Trips. Serving Our Fellow Beings
  • ZAKAAT AL-FITR COMPLEMENTS RAMADAAN In conjunction with the

    ZAKAAT AL-FITR COMPLEMENTS RAMADAAN In conjunction with the

    Allah Subhaanahu Wa Ta'aala by carrying out all of His Commands and avoiding all of His prohibitions. ... for one's own household, then it is encouraged to fulfill zakaat al-fitr according to the rate of those rice, which is RM21...
  • They that wait on the Lord shall mount

    They that wait on the Lord shall mount

    "They that wait upon the Lord shall renew their strength; They shall mount up with wings as Eagles"Isaiah 40:31. Wait {kaw-vaw'} means to bind together. Are you willing to "bind" your heart, soul, and mind together with God to accomplish...
  • Legal and Ethical Principles

    Legal and Ethical Principles

    A tort is broadly defined as a civil wrong committed against a person or property, excluding a breach of contract. (Personal Injury) Torts may be intentional (willful) or unintentional (accidental) and, if intentional, may also be crimes. Unintentional torts are...
  • Lecture 9 - Fatty Acid Metabolism

    Lecture 9 - Fatty Acid Metabolism

    Cellular uptake through the cyclic opening and closing of caveolae has been termed potocytosis. A "switchboard" for relaying signals from many extracellular chemical messengers into the cell's interior: Many membrane receptors important in signal mechanisms are concentrated in the caveolae...
  • Player Name: Karin Barrett  Team & Number: JV

    Player Name: Karin Barrett Team & Number: JV

    Started playing soccer at what age: 5. Favorite sports team outside of Mt. Hebron: US. Women's Soccer Team. Favorite quote: " My coach said I ran like a girl, I said if he could run a little faster he could...