SOLUTION: What is the primary interval of {{{80sin((x*pi/15) - pi/5) + 340}}} ?

Algebra ->  Trigonometry-basics -> SOLUTION: What is the primary interval of {{{80sin((x*pi/15) - pi/5) + 340}}} ?      Log On


   

Question 1081023: What is the primary interval of
80sin%28%28x%2Api%2F15%29+-+pi%2F5%29+%2B+340 ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
this function is periodic in x with period 30(ie one wavelength)
so, the "primary interval for this equation" is 30 units
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to calculate where it starts on x axis, we have
80sin%28%28x%2Api%2F15%29+-+pi%2F5%29+%2B+340 where A=80,B=pi%2F15,C=pi%2F5,and D=340


0%3C=+Bt%2BC+%3C=+2pi for any sinusoidal function
0+%3C=+%28pi%2F15%29t%2Bpi%2F5+%3C=2pi
0-pi%2F5%3C=%28pi%2F15%29t%2Bpi%2F5-pi%2F5%3C=2pi-pi%2F5
0-pi%2F5%3C=%28pi%2F15%29t%3C=10pi%2F5-pi%2F5
0-pi%2F5%3C=%28pi%2F15%29t%3C=+9pi%2F5
-pi%2F5%3C=%28pi%2F15%29t%3C=9pi%2F5


-3%3C=t+%3C=%289%2A15pi%29%2F%285pi%29
-3%3C=t+%3C=9%2A3
highlight%28-3%3C=t+%3C=27%29-> primary period

so, as you can see, the distance between -3 and 27 on x-axis is 30 units