Combining & Transforming Trig Functions - Help Needed

[astro_kat]

Trig Fuctions help! please

hi everyone,

my Trig textbook, is really vague and I'm not sure where i could find better information.

Basically, I'm not sure how to add, subtract, multiply, or divide trig functions. My text siad that to make a sinusoid the periods must be the same, and that the period is always 2 pi...? My book didn't even attempt to sauggest why--I'd really like to know what THE RULES FOR COMBINING AND TRANSFORMING TRIG FUNCTIONS ARE.

Thankyou to anyone who can send me in the right direction.

 

[Dick]

That's really a vague question. The rules for combining and transforming trig functions is the whole subject of 'trigonometry'. Can you be more specific?

 

[Architeuthis Dux]

Hello,

I understand your frustration with your textbook not providing clear information on combining and transforming trig functions. I can provide you with some general rules and guidelines that can help you understand these concepts better.

Firstly, when combining trig functions, it is important to remember that the periods must be the same. This is because the period of a trig function is the length of one full cycle of the function, and when adding or subtracting two functions, the periods need to align in order for the addition or subtraction to make sense.

For example, if you are adding sin(x) and cos(x), both of these functions have a period of 2π. This means that the addition will make sense because the cycles of the two functions will align perfectly. However, if you were to add sin(x) and cos(2x), the periods would not align (2π for sin(x) and π for cos(2x)), and the addition would not make sense.

When multiplying or dividing trig functions, the periods do not need to be the same. In these cases, you can use the general trig identities (such as sin^2(x) + cos^2(x) = 1) to simplify the expressions.

As for transforming trig functions, this involves changing the function's amplitude, period, or phase shift. The general rules for these transformations are as follows:

- Amplitude: multiplying the function by a constant changes its amplitude. For example, 2sin(x) would have an amplitude of 2 (twice the normal amplitude).
- Period: dividing the variable (x) by a constant changes the period. For example, sin(2x) would have a period of π (half the normal period).
- Phase shift: adding or subtracting a constant inside the function changes its phase shift. For example, sin(x+π/2) would have a phase shift of π/2 (shifted to the left by π/2).

I hope this helps to clarify the concepts of combining and transforming trig functions. You can also try looking for online resources or practice problems to further solidify your understanding. Keep practicing and don't give up, you'll get the hang of it!