Evaluating Trigonometric Expressions

In summary: I had a feeling the textbook and my teacher were using a different name for it. Thank you.In summary, the problem involves evaluating the derivative of h(x) = tan x on the interval [pi/4, 1] using the definition of the derivative. The set up for the calculation is [tan 1 - tan (pi/4)] / (1 - pi/4). This is a Mean Value problem, also known as an Average Rate of Change, where the gradient of the function at a point within the interval is equal to the Average Rate of Change. The Mean Value Theorem supports this concept.
  • #1
mathdad
1,283
1
Given h(x) = tan x, evaluate dh/dx on [pi/4, 1].

Note: d = delta

I need one or two hints. I can then try on my own.
 
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  • #2
RTCNTC said:
Given h(x) = tan x, evaluate dh/dx on [pi/4, 1].

Note: d = delta

I need one or two hints. I can then try on my own.
You'll have to do better than that. Are we required to use the Definition of the Derivative? Is this a Mean Value problem? How does one "evaluate" on a range?
 
  • #3
RTCNTC said:
Given h(x) = tan x, evaluate dh/dx on [pi/4, 1].

Note: d = delta

I need one or two hints. I can then try on my own.

$\dfrac{\Delta h}{\Delta x} = \dfrac{h(1) - h\left(\frac{\pi}{4}\right)}{1 - \frac{\pi}{4}}$

Note: learn some Latex ...
 
  • #4
tkhunny said:
You'll have to do better than that. Are we required to use the Definition of the Derivative? Is this a Mean Value problem? How does one "evaluate" on a range?

Skeeter got it. No derivative required. This question comes from my precalculus textbook by David Cohen. No calculus needed here. I was just not sure how to start the calculation. Like I said, Skeeter got it.
 
  • #5
Ok.

The set up is:

[tan 1 - tan (π/4)]/(1 - π/4)

I will do it tonight after work.
 
  • #6
So it is a Mean Value problem. Fair enough.
 
  • #7
tkhunny said:
So it is a Mean Value problem. Fair enough.

Is it more a rate of change problem?
 
  • #8
RTCNTC said:
Is it more a rate of change problem?

Right. An Average Rate of Change, aka Mean Value. Anyway it is done,
 
  • #9
It is done as far as this question is concerned. There are about 5 or 6 similar questions in Section 6.3 in my book that I can now do thanks to this site.
 
  • #10
tkhunny said:
Right. An Average Rate of Change, aka Mean Value. Anyway it is done,

An Average Rate of Change is NOT called a Mean Value.

The Mean Value Theorem states that the Average Rate of Change is equal to the gradient of the function at some point within the interval. It's poorly named too, as it is most likely not the "mean value" which gives that same gradient.
 
  • #11
Good information.
 

FAQ: Evaluating Trigonometric Expressions

1. What are trigonometric expressions?

Trigonometric expressions are mathematical expressions that involve trigonometric functions, such as sine, cosine, and tangent. These functions relate the angles of a triangle to the lengths of its sides.

2. How do you evaluate a trigonometric expression?

To evaluate a trigonometric expression, you must substitute the given values for the angles into the expression and use a calculator to find the numerical value of the expression.

3. What is the order of operations in evaluating trigonometric expressions?

The order of operations in evaluating trigonometric expressions is the same as in regular algebraic expressions: parentheses, exponents, multiplication and division, and finally addition and subtraction.

4. Can trigonometric expressions have more than one solution?

Yes, trigonometric expressions can have multiple solutions. This is because trigonometric functions are periodic, meaning they repeat their values after a certain interval. Therefore, an equation involving trigonometric functions may have more than one solution within a given interval.

5. How are trigonometric expressions used in real life?

Trigonometric expressions are used in various fields, such as engineering, physics, and navigation. They can be used to solve problems involving angles, distances, and other measurements in real-life situations. For example, they are used in calculating distances between two points, determining the height of a building, or designing bridges and buildings.

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