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)