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anonymous
 4 years ago
how can we calculate cos. 73 without a calculator?
anonymous
 4 years ago
how can we calculate cos. 73 without a calculator?

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1if you know that taylor polynomial for it ....

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.3without a calculator?? :)

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[cos(x)=cos(0)sin(0)x\frac{cos(0)}{2!}x^2+\frac{sin(0)}{3!}x^3+\frac{cos(0)}{4!}x^4+...\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1the odd powers go to zero, and the even powers go to 1/n! x^n alternating + and 

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0without a cal, yup :)

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1to clean it up: \[cos(x)=1\frac{1}{2}x^2+\frac{1}{24}x^4\frac{1}{720}x^6+\frac{1}{8!}x^8\frac{1}{10!}x^{10}+...\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1and I believe the 73 needs to be turned into radians by multiplying it by pi/180

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1i wonder if the newton method would be adaptable?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.3Pen and paper allowed? or not even?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0pen and paper allowed:) just no calculator

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1cos(73)=sin(17) is thats more doable

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.3So use the Taylor's series above. You can get answers to as accurately as the abacus allows. With pen and paper, you can get to quite a good degree of accuracy. You can also use the sum/difference formulas and double and half angle formulas to get approximations, and correct the difference using linearization. The question would be more complete if it specifies how many digits of accuracy are required. The answer would be different if 2 decimal digits are required (in that case, may be even mental calculation), 4 (pen and paper), 8 digits would require an abacus.

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.3You'll need to know how to calculate squareroots with pen and paper or by approximations, and know that pi=3.1415926535897932... cos(75)=(sqrt(6)sqrt(4))/4 sin(75)=(sqrt(6)+sqrt(4))/4 By linearization: dcos(x)/dx=sin(x) cos(x+d)=cos(x)+ (sin(x))*d where d=2 degrees in radians cos(73) =cos(752) =cos(75)sin(75)*(2pi/180) =(sqrt(6)sqrt(4))/4  (sqrt(6)+sqrt(4))/4 *(2*pi/180) =0.29254 Exact value = 0.29237

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.3sorry, corrections: cos(75)=(sqrt(6)sqrt(2))/4 sin(75)=(sqrt(6)+sqrt(2))/4 ... =(sqrt(6)sqrt(2))/4  (sqrt(6)+sqrt(2))/4 *(2*pi/180)
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