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Name: Date: Page 1 of 5 Activity 6.6.3 Angle Sum and Difference Formulas (+) sin(π + π) = π πππ β πππ π + πππ π β π πππ cos(π + π) = cos(π) cos(π) β sin(π) sinβ‘(π) tan(π + π) = β‘ π‘πππ + π‘πππ 1 β π‘πππ β π‘πππ sin(π β π) = π πππ β πππ π β πππ π β π πππ cos(π β π) = cos(π) cos(π) + sin(π) sinβ‘(π) tan(π β π) = β‘ π‘πππ β π‘πππ 1 + π‘πππ β π‘πππ Do not use a calculator for this activity. 1. Use 120° and 45° to find exact values for the following trigonometric functions. a. sin(165°) b. cos(165°) c. tan(165°) Activity 6.6.3 Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 2 of 5 2. Find exact values for the following: a. sin(75°) b. cos(75°) c. tan(75°) 3. Show that you used an angle sum or difference formula to find exact values for the following: 7π a. π ππ 12 Activity 6.6.3 βπ b. πππ 12 Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 3 of 5 c. π‘ππ105° 4. Derive the double angle formula for sine and cosine. Note sin(2a) that can be written sin(a + a) a. Use the angle sum formula to expand sin(2a) using the angle sum formula and simplify. b. Use the angle sum formula to expand cos(2a) and simplify. Activity 6.6.3 Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 4 of 5 c. Write the double angle formula for sine and the double angle formula for cosine: d. Verify an instance of the double angle formula for cosine by evaluating each side of the equation and showing it is true: cos(60°) = cos2(30°) β sin2(30°) 5. Simplify the following, give exact values. Do this without a calculator. a. sin(10°β‘) β cos(40°β‘) β cosβ‘(10°β‘) β sinβ‘(40°β‘) 9π 11π 9π 11π b. cos( 8 ) cos( 24 ) + sin( 8 ) sin( 24 ) Activity 6.6.3 Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 5 of 5 c. 2 sin°15·cos15° 5π 5π 5π 5π d. cos2( 8 ) β sin2( 8 ) e. cos2( 8 ) + sin2( 8 ) π 5π π 5π f. sin (12β‘) β cos (β‘ 12 ) + cosβ‘(12β‘) β sinβ‘( 12 β‘) π‘ππ25°+π‘ππ200° g. 1βπ‘ππ25°βπ‘ππ200° Activity 6.6.3 Connecticut Core Algebra 2 Curriculum Version 3.0