# How do you use trigonometric substitution to write the algebraic expression #sqrt(64-16x^2)# as a trigonometric function of #theta# where #0<theta<pi/2# and #x=2costheta#?

However, the expression needs to be positive because this is in the first quadrant.

Thus:

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To express ( \sqrt{64 - 16x^2} ) as a trigonometric function of ( \theta ), where ( 0 < \theta < \frac{\pi}{2} ) and ( x = 2 \cos(\theta) ), follow these steps:

- Rewrite ( x = 2 \cos(\theta) ) in terms of ( \theta ) to express ( x ) as a trigonometric function.
- Substitute the expression for ( x ) into ( \sqrt{64 - 16x^2} ).
- Simplify the expression using trigonometric identities.
- Determine the appropriate trigonometric function of ( \theta ) that represents ( \sqrt{64 - 16x^2} ) in the given interval.

By following these steps, you can express ( \sqrt{64 - 16x^2} ) as a trigonometric function of ( \theta ) within the specified domain.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you evaluate if possible the 6 trigonometric functions of the real number #t= (-2pi)/3#?
- How to convert 70 degrees into radians?
- How do you evaluate #sin(pi+pi/6)#?

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