what's amplitude and period for domain and range and how do you find the turning point of a Sine cos and tan graph?

Question

what's amplitude and period for domain and range and how do you find the turning point/point of inflection of  Sine cos and tan graphs?

Answer 1

TThe amplitude of a sine graph is the coefficient of the sine function. Notice that the amplitude of sin(x) is 1, and sin/x has range from y=-1 to y=1. So top to bottom the length is 2. Divide by 2 to get the amplitude. This gives us a way of calculating the amplitude of any sine graph if we don't have the function written. Calculate the difference between the max and min of the range, and divide by 2. 

 

Now the turning points, find the critical points where the first derivative is 0 (generally 0 or undefined) and use either the first or second derivative test to see whether the point is at a max or min. 

 

Now the point of inflection, calculate the second derivative and check when it's equal to 0.

 

I hope that helped!

 

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