1)how do you simplify 3xcos5x using trigometric functions
2)how do you simplify sin2xcos4x using trigometric functions
don't know what you mean by "simplify". They're already pretty simple.
I see no way to rewrite 3x cos5x
sin2x cos4x = (sin6x + sin2x)/2
but that doesn't look any simpler to me.
any further clarification?
how did you do sin2x cos4x = (sin6x + sin2x)/2 what os the formula I need to use
Steve help please
use the trig sum-to-difference formulas
sinAcosB = (sin(A+B) + sin(A-B))/2
You must have seen such. If not a visit to
http://oakroadsystems.com/twt/sumdiff.htm
bears study
cos3xcos5x
how do rewrie this using trigmetric finctions Steve thanks
come on - give it a try using the formulas. What do you come up with?
(cos8x+cos2x)/2 steve is it right
steve
To simplify the expression 3x cos(5x) using trigonometric functions, we can use the trigonometric identity:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
Let's use this identity to break down the expression step by step:
1) Start with 3x cos(5x)
2) Rewrite cos(5x) as cos(x + 4x) to apply the identity
3) Apply the identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
to cos(x + 4x):
cos(x + 4x) = cos(x)cos(4x) - sin(x)sin(4x)
4) Substitute this back into the original expression:
3x cos(5x) = 3x(cos(x)cos(4x) - sin(x)sin(4x))
So, the simplified expression for 3x cos(5x) using trigonometric functions is 3x(cos(x)cos(4x) - sin(x)sin(4x)).
Similarly, to simplify the expression sin(2x)cos(4x) using trigonometric functions, we can use the trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
Let's use this identity to break down the expression step by step:
1) Start with sin(2x)cos(4x)
2) Rewrite sin(2x) as sin(x + x) to apply the identity
3) Apply the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
to sin(x + x):
sin(x + x) = sin(x)cos(x) + cos(x)sin(x)
4) Substitute this back into the original expression:
sin(2x)cos(4x) = (sin(x)cos(x) + cos(x)sin(x))cos(4x)
So, the simplified expression for sin(2x)cos(4x) using trigonometric functions is (sin(x)cos(x) + cos(x)sin(x))cos(4x).