Formulas for functions | Trigonometric Logarithmic Hyperbolic functions.

**Formulas for trigonometric, logarithmic and hyperbolic functions**

Now here I give a collection of formulas for trigonometric, logarithmic and hyperbolic functions. Later I’ll use them a lot to solve the problems.

**1. Trigonometric functions – formulas**

First of all, it’s the formulas for trigonometric identities.

**1.1 Formulas for trigonometric identities**

So these are as follows:

Now comes the next one as

Finally, it’s with the cot function as

Also, I have used the formulas in trigonometric identities a lot in **integration****.**

Next, comes the formulas of the sum and difference identities.

**1.2. Sum and difference identities**

First of all, it’s the sum and difference identities of the sine function. So the formula for the sine function of the sum of two angles and is

Also, the formula for the sine function of the difference of two angles and is

Next, comes the sum and difference identities of the cosine function. So these are

and

Finally, comes the sum and difference identities of the tan function. So these are

and

Now comes the double angle formulas for sine, cosine, tan and cot functions.

**1.3. Double angle formulas**

First of all, it’s the sine function. So it is as follows:

Next, comes the cosine function. So that gives

Then comes the tan function. So I can say that

Finally, it’s the cot function. So that gives

**2. Logarithmic functions – formulas**

First of all, I write some basic information about logarithmic functions. So means

Similarly, means

From now onwards, I’ll write the formulas for Also, these hold true for as well.

**2.1. Adding two logarithmic functions**

When I add two logarithmic numbers, it gives an interesting result. So it gives

But also remember that

**2.2. Subtracting one logarithmic function from the other**

When I subtract one logarithmic function from the other, it means something completely different. So that gives

But also remember that

**2.3. Values of some standard / frequently used logarithmic functions**

Now I’ll give the values of some standard or frequently used logarithmic functions. So these are as follows:

Also, I can say that

**2.4. The logarithm of functions like **

Now let’s suppose that I have a function like . Then the natural logarithm of will be

So I can rewrite it as

Similarly, if a function has the form the natural logarithm of will be

So I can say that

**Special case**

If then the natural logarithm of will be

Also, from section 2.3 I already know that . Thus will be

So I can say that

**3. Hyperbolic functions **

**3.1 Definition **

- Now the hyperbolic sine of is
- Also, the hyperbolic cosine of is
- Next, the hyperbolic tangent of is
- Then the hyperbolic cotangent of is
- Similarly, the hyperbolic secant of is
- Again the hyperbolic cosecant of is

**3.2 Formulas for hyperbolic functions by definition**

Now, by definition, is

Also, will be

So will be

Then will be

**3.3. Formulas for hyperbolic identities**

**3.4 Functions of negative arguments**

**3,5 Addition and subtraction formulas**

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