Calculate the phase angle between two sinusoids

• DryRun
In summary, the conversation discusses the calculation of phase difference between two equations, v1(t) = -10sin(wt+140) and v2(t) = 12sin(wt-10). The negative sign in front of the 10 causes confusion in finding the phase angle, as it changes the direction of the vector. The conversation ends with a question about the solution to this problem.
DryRun
Gold Member
Homework Statement
Calculate the phase angle between two sinusoids.
Relevant Equations
v1(t) = -10cos(wt + 50) and v2(t) = 12sin(wt-10)
I am trying to do exactly what was stated, by finding it with calculations only, so, without having to draw the curves. Is that possible?

Here is my attempt:

v1(t) = -10cos(wt + 50) and v2(t) = 12sin(wt-10)
v1(t) = -10cos(wt + 50) becomes v1(t) = -10sin(wt+50+90) = v1(t) = -10sin(wt+140)

Now, i have these equations: v1(t) = -10sin(wt+140) and v2(t) = 12sin(wt-10).
If there was no negative sign in front of the 10, then i could have simply found the phase angle by: 140--10 = 150 degrees, but since it has a negative sign, I'm not sure what to do.

What is the phase difference of (multiplying by negative)? Think of a vector pointing in a direction. Now think of the "negative" of that vector. What's the angle between those vectors?

SammyS and Delta2
Did you figure it out @DryRun ?

1. What is the definition of phase angle between two sinusoids?

The phase angle between two sinusoids refers to the difference in the starting point of their respective cycles. It is measured in degrees or radians and determines how the two sinusoids are aligned in relation to each other.

2. How is the phase angle calculated?

The phase angle can be calculated by finding the difference between the phase shift of the two sinusoids. This can be done by determining the starting point of each sinusoid's cycle and subtracting the smaller value from the larger value. The result will be the phase angle in degrees or radians.

3. What does a positive phase angle indicate?

A positive phase angle indicates that the two sinusoids have a forward or in-phase relationship, meaning they have the same frequency and their cycles align in the same direction.

4. What does a negative phase angle indicate?

A negative phase angle indicates that the two sinusoids have a backward or out-of-phase relationship, meaning they have the same frequency but their cycles align in opposite directions.

5. How can the phase angle be used in real-world applications?

The phase angle can be used in fields such as signal processing, electrical engineering, and physics to analyze and manipulate signals and waves. It is also used in music production to create specific sound effects and in astronomy to measure the positions of celestial bodies.

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