SUM & DIFFERENCE FORMULAS

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Presentation transcript:

SUM & DIFFERENCE FORMULAS

SUM & DIFFERENCE FORMULAS cont’d.

Ex. Use the sum & difference identities to find the EXACT value of each function…this means answers will be fractions perhaps with Radicals…NOT decimals! 1. cos 75˚

Ex. Use the sum & difference identities to find the EXACT value of each function…this means answers will be fractions perhaps with Radicals…NOT decimals! 1. cos 160˚cos40˚+sin160˚sin40˚ A 120˚ is a 60˚ in the 2nd quadrant.

Ex. If A & B are the measures of two first quadrant angles, find the exact value of each function. 1. If sinA=12/13 and cosB=3/5 , find cos (A-B). 13 12 5 4 A B 5 3 Recall: cos (A-B)=cosAcosB+sinAsinB So, we need: CosA & sinB which means we use pythag. Thm. 122+b2=132 results in b=5 So, cosA= 5/13 a2+32=52 results in a=4 So, sinB= 4/5 cos (A-B)=(5/13)(3/5)+(12/13)(4/5) cos (A-B)=63/65

Ex. Use the sum & difference identities to find the EXACT value of each function…this means answers will be fractions perhaps with Radicals…NOT decimals! 2. tan 345˚

DOUBLE- & HALF-ANGLE FORMULAS. Double Angle or

DOUBLE- & HALF ANGLE FORMULAS cont’d