Clarification of RSin(x+a), RCos(x+a)

  • Thread starter thomas49th
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In summary, the conversation discusses whether it is possible to turn a given function, y = 3Sin2x + 4cos2x, into expressions of the form RSin(x+a) and RCos(x+a). The conclusion is that it is possible as long as the values of 'b' are the same, and in that case, either Rsin(bx+A) or Rcos(bx+A) can be used. However, this is not possible for the function y = 3Sin2x + 4cos4x.
  • #1
thomas49th
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Homework Statement


I want to clarify about using RSin(x+a) and RCos(x+a) for aSinbx + cCosbx

If I am given y = 3Sin2x + 4cos2x

Can I turn it into RSin(x+a) and RCos(x+a) expressions

HOWEVER

if y = 3Sin2x + 4cos4x Can I turn it into RSin(x+a) and RCos(x+a) expressions?

Thanks :)
 
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  • #2
No, you can't. Try plotting that function. It doesn't look very much like a simple sin or cos graph, does it?
 
  • #3
Dick said:
No, you can't. Try plotting that function. It doesn't look very much like a simple sin or cos graph, does it?

is that for

if y = 3Sin2x + 4cos4x

what about:

"I want to clarify about using RSin(x+a) and RCos(x+a) for aSinbx + cCosbx

If I am given y = 3Sin2x + 4cos2x

Can I turn it into RSin(x+a) and RCos(x+a) expressions"

or can you only do one or the other (either RSin(x+a) and RCos(x+a)) and you have to spot each one


Thanks :)
 
  • #4
For asinbx+cCosbx, once those 'b's are the same, you can turn it into either Rsin(bx+A) or Rcos(bx+A).
 
  • #5
cool cheers :)
 

1. What is the difference between RSin(x+a) and RCos(x+a)?

RSin(x+a) and RCos(x+a) are both trigonometric functions that involve the sum of an angle (x) and a constant (a). The main difference between the two is that RSin(x+a) returns the sine of the sum of x and a, while RCos(x+a) returns the cosine of the sum of x and a.

2. What is the purpose of the "R" in RSin(x+a) and RCos(x+a)?

The "R" in RSin(x+a) and RCos(x+a) stands for "resultant" and is used to indicate that the function returns the overall result of the calculation, rather than just the sine or cosine value of the angle (x+a).

3. How do I solve for x in "RSin(x+a) = RCos(x+a)"?

To solve for x in this equation, you can use the trigonometric identity "tan(x) = sin(x) / cos(x)" to rewrite the equation as "tan(x+a) = R". Then, you can use the inverse tangent function to find the value of (x+a), and subtract a from that value to find the value of x.

4. Can RSin(x+a) and RCos(x+a) be simplified?

Yes, RSin(x+a) and RCos(x+a) can be simplified using trigonometric identities. For example, the sum formula for sine (sin(x+y) = sin(x)cos(y) + cos(x)sin(y)) can be used to simplify RSin(x+a) to R(sin(x)cos(a) + cos(x)sin(a)), and similarly for RCos(x+a).

5. What is the period of RSin(x+a) and RCos(x+a)?

The period of RSin(x+a) and RCos(x+a) is 2π, which means that the function repeats itself every 2π units on the x-axis. This is because the period of sine and cosine functions is 2π, and adding a constant (a) does not affect the period.

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