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C3: maximum and minimum values watch

1. I am really struggling with these types of questions where they ask you to work out what the maximum value of a trig function is and at what x-value it occurs etc.

Would anyone be able to explain the theory behind this so I can understand these ques and work them out properly?

Eg:

Sin3X= 3sinx - 4sin^3x

Determine the greatest posible value of:

9 sin(10/3a) - 12 sin^3(10/3a)

Apologies as i dont know how to use latex.
2. (Original post by major-major-major)
I am really struggling with these types of questions where they ask you to work out what the maximum value of a trig function is and at what x-value it occurs etc.

Would anyone be able to explain the theory behind this so I can understand these ques and work them out properly?

Eg:

Sin3X= 3sinx - 4sin^3x

Determine the greatest posible value of:

9 sin(10/3a) - 12 sin^3(10/3a)

Apologies as i dont know how to use latex.
If you mean the and

Then the maximum value or minimum value is just 1 x R of the function. It is derived from the original and graphs

EDIT: actually I've misread! For your example, it would be , so hence you want the maximum value of

I would think the answer is 3
3. (Original post by .:excel4100%:.)
If you mean the and

Then the maximum value or minimum value is just 1 x R of the function. It is derived from the original and graphs

So then how would you solve the equation above?
4. you first draw a sin/cos graph, and see where the first max/min occur....in a sin graph your first max occurs at 90degrees

so you do: x-Theta=90
x= 90+Theta for you max etc
5. The answer to the above question is 9. I have no idea how to do these questions. !!!!!!!!!!!!!!!!!!!!!
6. (Original post by major-major-major)
The answer to the above question is 9. I have no idea how to do these questions. !!!!!!!!!!!!!!!!!!!!!
The answer would be 3. This is when sine of the angle is -1.

-9 - (-12) = 3.

When sine of the angle is 1, you get: 9 - 12 = -3

When sine of the angle is 0, you get: 0 - 0 = 0

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