How Do You Determine the Period of a Combined Sinusoid in Trigonometry?

[astro_kat]

Hiya,

I'm really curious to know the rules of combining trig functions, say if:
y = sin(x) + cos(2x)
_How would I determine the period of the sinusoid (if it IS one)

Is there a mthod of predicting if two sinusoids will compose another sinusoid, if there is I'm missing it. My textbook says that 2*pi is always a good solution to check for, but what does that mean? How do I check?
In the end, I really need a better means of learning Trig, my text makes too many conjectures w/o backing any of them up.

Any hyelp woudl be appreciated!

 

[rock.freak667]

Well you can use the factor formula of

$$SinP+sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})$$ and use the fact that sinx=cos(pi/2 -x)

 

[Architeuthis Dux]

I can understand your confusion and frustration with conceptual trigonometry. Trigonometry is a complex branch of mathematics that deals with the relationships between angles and sides of triangles. It is often used in fields such as physics, engineering, and astronomy to solve problems involving angles and distances.

To determine the period of a sinusoid such as y = sin(x) + cos(2x), you can use the following formula: Period = 2π/b, where b is the coefficient of x in the trig function. In this case, the coefficient of x is 2, so the period would be 2π/2 = π. This means that the sinusoid will repeat itself every π units.

There is a way to predict if two sinusoids will compose another sinusoid, known as the sum and difference identities. These identities state that sin(a) + sin(b) = 2sin((a+b)/2)cos((a-b)/2) and cos(a) + cos(b) = 2cos((a+b)/2)cos((a-b)/2). By using these identities, you can simplify the expression and see if it can be written as a single sinusoid. In the case of y = sin(x) + cos(2x), you can use the first identity to rewrite it as 2sin((x+2x)/2)cos((x-2x)/2) = 2sin(3x/2)cos(-x/2) = sin(3x). This means that the two sinusoids have composed to form a single sinusoid with a period of 2π/3.

As for your textbook, it is important to have a strong foundation in basic trigonometric concepts before attempting to understand more complex concepts. I would recommend seeking additional resources, such as online tutorials or practice problems, to help you better understand the material. It is also important to always question and verify the conjectures presented in your textbook, as this will help deepen your understanding of the subject. Keep practicing and seeking help when needed, and eventually, you will develop a strong understanding of trigonometry.