SOLUTION: if sin(x)+cos(x)=1/2 then find the values : (1) sin(x)*cos(x) (2) sin^2(x)+cos^2(x) (3) sin^3(x)+cos^3(x) thank you in advance

Algebra ->  Trigonometry-basics -> SOLUTION: if sin(x)+cos(x)=1/2 then find the values : (1) sin(x)*cos(x) (2) sin^2(x)+cos^2(x) (3) sin^3(x)+cos^3(x) thank you in advance       Log On


   

Question 1083298: if sin(x)+cos(x)=1/2 then find the values :
(1) sin(x)*cos(x)
(2) sin^2(x)+cos^2(x)
(3) sin^3(x)+cos^3(x)
thank you in advance
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
(1) sin(x)*cos(x)
Given: sin%28x%29%2Bcos%28x%29=1%2F2

Square both sides:

sin%5E2%28x%29%2B+2sin%28x%29cos%28x%29%2B+cos%5E2%28x%29=1%2F4

sin%5E2%28x%29%2B+cos%5E2%28x%29+%2B+2sin%28x%29cos%28x%29=1%2F4

%28sin%5E2%28x%29%2B+cos%5E2%28x%29%5E%22%22%29+%2B+2sin%28x%29cos%28x%29=1%2F4

1%2B2sin%28x%29cos%28x%29=1%2F4

2sin%28x%29cos%28x%29=-3%2F4

sin%28x%29cos%28x%29=-3%2F8

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(2) sin^2(x)+cos^2(x)
That's just 1.

-----------------------------------
(3) sin^3(x)+cos^3(x)
Factor as the sum of two cubes:



Plug in the values from above parts:

%281%2F2%29%281-%28-3%2F8%29%5E%22%22%29

%281%2F2%29%281%2B3%2F8%29

%281%2F2%29%2811%2F8%29

11%2F16

Edwin