Simplify the following expressions and evaluate.
sin(5π/8)cos(3π/8) - cos(5π/8)sin(3π/8)
2007-01-13 13:46:59 · 6 answers · asked by omg123123166 1 in Science & Mathematics ➔ Mathematics
sin(5π/8)cos(3π/8) - cos(5π/8)sin(3π/8)
= sin(5π/8 - 3π/8)
= sin(2π/8)
= sin(π/4)
=sqrt(2)/2
2007-01-13 13:58:35 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
This is an angle subtraction formula.
sin(a - b) = (sin a)(cos b) - (cos b)(sin a)
In this case:
sin(5π/8)cos(3π/8) - cos(5π/8)sin(3π/8) = sin(5π/8 - 3π/8)
= sin(π/4) = 1/√2
2007-01-13 14:18:54 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
Sin(A)Cos(B)-Cos(A)Sin(B)=Sin(A-B)
sin(5π/8)cos(3π/8) - cos(5π/8)sin(3π/8)= Sin(5π/8-3π/8)
=Sin(π/4)
=0.707
2007-01-13 14:00:25 · answer #3 · answered by Rajkiran 3 · 0⤊ 0⤋
this expression is of the form ...
sin (s – t) = sin s cos t – cos s sin t
= sin(5*pi/8 - 3*pi/8)
= sin (pi /4) = 0.707
2007-01-13 14:01:35 · answer #4 · answered by aswan k 1 · 0⤊ 0⤋
this equation is basically sin(a)cos(b) - cos(a)sin(b), which is the expanded form of sin(a-b)...
SO it would become sin(5pi/8 - 3pi/8) which is sin (pi/4) which is sin 45, which is root2/2!!!
so the answer is (root 2)/2
2007-01-13 13:58:25 · answer #5 · answered by Anonymous · 0⤊ 0⤋
sin(a-b)= sina*cosb-cosa*sinb
so sin(5pi/8-3pi/8)= sin(pi/4) = (sqrt2)/2
2007-01-13 13:57:56 · answer #6 · answered by santmann2002 7 · 0⤊ 0⤋