Final answer:
The equation 460sin(314t+30°) does not become 460L-60°; instead, it represents a sinusoidal function. To solve an equation with two unknowns like T1 sin (30°)+T2 sin (45°) = w, express one variable in terms of the other, substitute it into the original equation, and then solve for the single unknown.
Step-by-step explanation:
To address the student's question, let's clarify that 460sin(314t+30°) does not simplify to 460L-60°; instead, it is an equation representing a sinusoidal function in terms of time, t, with a phase shift. When dealing with equations like T₁ sin (30°)+T₂ sin (45°)= w, having two unknowns, T₁ and T₂, it's possible to solve for one variable in terms of another to obtain a single equation with one unknown.
If you have an expression that relates T₂ to T₁, you can substitute this into the original equation. For instance, if T₂ is expressed as a function of T₁, such as T₂ = kT₁ where k is a constant, you can then replace T₂ in your equation to get T₁ sin (30°) + (kT₁) sin (45°) = w. This simplifies the problem to solving for T₁ alone. To solve this, you'd combine the terms involving T₁ and then solve for T₁ using algebraic methods.