how do you find the period of 2sin(2x) + 3cos(3x), and hence any 'addition of trig function' (with sin & cos) graph?

thanks!!

To find the period of a function containing more than one trig term, this is one option:

**1. Find the period of each term,**ie. 2sin(2x) is π and 3cos(3x) is 2π/3 (from the period formula 2π/n, sin(nx) or cos(nx))

*Converting into degrees will make the lowest common denominator (LCD) calculation easier***2. Convert each result to degrees,**ie. 180° and 120° respectively (from the radian to degree formula 180x/π where x is the radian angle)

*Step 3 and 4 is finding the lowest common denominator between the degree angles***3. Decompose each degree angle into its prime parts,**ie.

180 --> 18*10 --> 9*2*5*2 --> 2*2*3*3*5

120 --> 12 * 10 --> 4*3*5*2--> 2*2*2*3*5

**4. Group these primes together, removing sequences that contain less of a given number.**ie. 2*2 vs. 2*2*2 (choose 2*2*2 as it contains more 2's)

3 vs. 3*3 (choose 3*3 as it contains more 3's)

*The end result will be the group 2*2*2*3*3*5, which equals 360°**Optional: If you are required to have the degrees in radians***5. Convert the degree result back into radians, (using the degree to radian formula πx/180, where x is the degree angle)**ie. 360° becomes 2π radians

**6. This result, 2π or 360° is your period of the function: 2sin(2x) + 3cos(3x)**For some intuition, you can think of it like this:

If I count from 1 to 3 and simutanously a buddy counts 4-5. The pattern will repeat (the period) after the 6th count (2*3 from the LCD process)

**1** 2 3 1 2 3

**1****4** 5 4 5 4 5

**4**This is essentially the same concept.

Hope this helps