Honors Precalculus

Mr. Velazquez

Trigonometry:

Sum and Difference Identities

Sum and Difference Formulas for Sine and Cosine

Sum and Difference Formulas for Sine and Cosine

Prove that cos𝜋

2− 𝜃 = sin 𝜃

Sum and Difference Formulas for Sine and Cosine

Verify the identity: cos 𝜋 − 𝜃 = −cos 𝜃

Sum and Difference Formulas for Sine and Cosine

Find the exact value for: cos 100 ° cos 55° + sin 100° sin 55°

Sum and Difference Formulas for Sine and Cosine

Find sin 75° (given that 75° = 30° + 45°)

Sum and Difference Formulas for Sine and Cosine

Find sin 15° (given that 15° = 45° − 30°)

Sum and Difference Formulas for Sine and Cosine

Suppose that cos 𝜃 = − 35 for an angle 𝜃 in quadrant II, and

cos 𝛽 = 1213 for an angle 𝛽 in quadrant I. Find the exact value

of each of the following:

1. sin 𝜃

2. sin 𝛽

3. sin 𝜃 + 𝛽

3. cos 𝜃 + 𝛽

Sum and Difference Formulas for Tangent

EXTRA CREDIT: (10 POINTS)

Use the sum and difference identities for sine and

cosine to prove the sum and difference formulas

for tangent. (Remember tan 𝜃 =sin 𝜃

cos 𝜃)

Sum and Difference Formulas for Tangent

Simplify: tan(𝜋 − 𝜃)

Sum and Difference Formulas for Tangent

Simplify: tan(5𝜋 4 + 𝜃)

Exit Ticket: Sum and Difference Identities

Suppose that 𝐜𝐨𝐬𝜶 = − 𝟑𝟒 (for an angle 𝛼 in quadrant II) and

that 𝐬𝐢𝐧𝜷 = 𝟓𝟔 (for an angle 𝛽 in quadrant I). Use this

information to find the exact values for the following:

(a) 𝐬𝐢𝐧𝜶

(b) 𝐜𝐨𝐬𝜷

(c) 𝐬𝐢𝐧(𝟐𝜶)

(d) 𝐜𝐨𝐬(𝜶 − 𝜷)

(e) 𝐭𝐚𝐧(𝜶 + 𝜷)

Homework: (DUE 2/26)

Pg. 603, #4-56

(mult. of 4)