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Advanced Math/Trigonometry- exact values
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Question
Using exact values, find:
a. tan 105 degrees
b. sin 255 degrees
Thank you for all your help!
a.)
tan(105) =
tan(60 + 45) =
(tan(60) + tan(45))/(1 - tan(60)tan(45) =
(sqrt(3) + 1)/(1 - sqrt(3)) =
Multiply top and bottom by 1 + sqrt(3)
((1 + sqrt(3))(1 + sqrt(3)))/(1 - 3) =
(1 + 2sqrt(3) + 3)/-2 =
(4 + 2sqrt(3))/-2 =
-2 - sqrt(3) or about -3.7321
-------------------------------------
b.)
sin(255) =
sin(-105) =
sin(-60 - 45) =
sin(-(60 + 45)) =
-sin(60 + 45) =
-(sin(60)cos(45) + sin(45)cos(60)) =
-((sqrt(3)/2)(sqrt(2)/2) + ((sqrt(2)/2)(1/2))) =
-((sqrt(6)/4) + (sqrt(2)/4)) =
-((sqrt(6) + sqrt(2))/4 or about -.9659
info found at http://math2.org/math/trig/identities.htm
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