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Activity 7: Investigating Compound Angles Click the picture to continue D A B C Activity 7: Investigating Compound Angles •In the introduction of the activity, we conclude that the best way to find the exact value of sin75o was to write is as a sum of two angles: sin(75) sin(30 45) •We know that: sin 6 4 1 sin 6 2 2 sin 2 4 •So, if: sin then, 6 4 2 1 2 1 sin 1.207 2 2 6 4 2 Activity 7: Investigating Compound Angles •When we try to get an approximate value on the calculator we get: sin 6 4 0.966 •Why do we get two different answers? •We have to graph this angle in standard position to verify which answer is correct. Activity 7: Investigating Compound Angles •Let us place this angle in standard form where radius is 1: y 1 β π/6 π/4o 75 sin(π/6)cos(π/4) sin(π/4)cos(π/6) HYPOTENUSE π/4 OPPOSITE Therefore, We use the cosine ratio: Given the angles inright the We can solve for this right are now going to create Since The altitude we are of trying the to find Split Using the simple angle geometry into radian and To solve for the second o)=sin(π/6+ sin(75 π/4) smallest triangle, itour isπ/6 triangle we have aaltitude right triangle inside the ratio created sin(π/6+ with π/4), the we angles creating ofsince aright π/6 pair + of π/4. parallel This is we must find the cos(π/4)=AD/HY o calculate othe now possible to the angle, π/6 and compound angle where should angle π/4 identify can be the solved sides the lines same we see as 45 that and the 30 blue .we dot denoted by the blue sin(π/6)cos(π/4)+sin(π/4)cos(π/6) cos(π/4)=Altitude/sin(π/6) altitude. hypotenuse of right angle on the end need since in itsorder hypotenuse to1.this solve is this The and the red isstart dot now must ausing sum up dot Whenangle we calculate special of the green arrow. ratio. cos(π/6). compound to 90o.sin(angle)=OP/HY. Based angle. on alternate angles: Altitude=sin(π/6)cos(π/4) 2 blue x angles, 1 2 the 3 dot must be 2 2 2 2 to π/4 rads. equal =0.966 This is the answer we got on the calculator Activity 7: Investigating Compound Angles •In general, when finding the sine ratio of a compound angle as shown below: sin(A+B) = sinAcosB + sinBcosA B sinAcosB+sinBcosA A Activity 7: Investigating Compound Angles •Go back to the activity website and complete the rest of the activity online!