The phasor technique makes it pretty easy to combine several sinusoidal functions into a single sinusoidal expression without using trigonometric identities. however, you cannot use the phasor technique in all cases.

Select the expressions below for which the phasor technique cannot be used to combine the sinusoids into a single expression. check all that apply.

a.−100sin(10,000t+90∘)+40sin(10,100 t− 80∘)+80cos(10,000t)

b.100cos(500t+40∘)+50sin(500t−120∘) −120cos(500t+60∘)

c.25cos(50t+160∘)+15cos(50t+70∘)

d.45sin(2500t−50∘)+20cos(1500t+20∘)

e.75cos(8t+40∘)+75sin(8t+10∘)−75cos (8 t+160∘)

Expressions a and d cannot be combined using phasor technique:

Explanation:

We use phasor technique to perform several operations on sinusoidal functions. In order to apply phasor technique, first we have to check whether the expression has same frequency throughout or not.

Let us analyze each given expression.

a. −100sin(10,000t+90∘) + 40sin(10,100t− 80∘) + 80cos(10,000t)

As you can see in the above expression, there is a difference between frequencies. 10,000 and 10,100 therefore, this expression cannot be combined into a single wave using phasor technique.  

b. 100cos(500t+40∘) + 50sin(500t−120∘) −120cos(500t+60∘)

As you can see in the above expression, the frequency is same in each wave 500, therefore, we can apply phasor technique on this expression.  

c. 25cos(50t+160∘) + 15cos(50t+70∘)

As you can see in the above expression, the frequency is same in each wave 50, therefore, we can apply phasor technique on this expression.  

d. 45sin(2500t−50∘) + 20cos(1500t+20∘)

As you can see in the above expression, there is a difference between frequencies. 2500 and 1500 therefore, this expression cannot be combined into a single wave using phasor technique.  

e. 75cos(8t+40∘)+75sin(8t+10∘)−75cos(8t+160∘)

As you can see in the above expression, the frequency is same in each wave 8, therefore, we can apply phasor technique on this expression.  

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