In mathematics, sine and cosine series are called infinite series and they are very important concepts. In this article, you learn to write a program in c to compute the sine and cosine series. First of all, a cosine of 180 degrees should be equal to -1, so the result you got is right. Secondly, you sometimes can't get exact values when using sin/cos/tan etc functions as you always get results that are the closest to the correct ones. In your case, the value you got from sin is the closest to zero. C/C provides sin(a), cos(a). First of all, a cosine of 180 degrees should be equal to -1, so the result you got is right. Secondly, you sometimes can't get exact values when using sin/cos/tan etc functions as you always get results that are the closest to the correct ones. In trigonometrics, arc cosine is the inverse operation of cosine. Header provides a type-generic macro version of this function. This function is overloaded in (see valarray acos ).

This function is overloaded in and (see complex sin and valarray sin). Additional overloads are provided in this header ( ) for the integral types: These overloads effectively cast x to a double before calculations (defined for T being any integral type ).

For any triangle:

The Law of Cosines (also called the Cosine Rule) says:

c² = a² + b² − 2ab cos(C)

It helps us solve some triangles. Let's see how to use it.

Example: How long is side 'c' ... ?

We know angle C = 37º, and sides a = 8 and b = 11

Answer: c = 6.67

How to Remember

How can you remember the formula?

Well, it helps to know it's the Pythagoras Theorem with something extra so it works for all triangles:

So, to remember it:

• think 'abc': a² + b² = c²,
• then a 2nd 'abc':2ab cos(C),
• and put them together: a² + b² − 2ab cos(C) = c²

When to Use

The Law of Cosines is useful for finding:

• the third side of a triangle when we know two sides and the angle between them (like the example above)
• the angles of a triangle when we know all three sides (as in the following example)

Example: What is Angle 'C' ...?

The side of length '8' is opposite angle C, so it is side c. The other two sides are a and b.

Now let us put what we know into The Law of Cosines:

Now we use our algebra skills to rearrange and solve:

Dev C++ 5.11

In Other Forms

Easier Version For Angles

We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the 'direct' formula (which is just a rearrangement of the c² = a² + b² − 2ab cos(C) formula). It can be in either of these forms:

cos(C) = a² + b² − c²2ab

cos(A) = b² + c² − a²2bc

cos(B) = c² + a² − b²2ca

Example: Find Angle 'C' Using The Law of Cosines (angle version)

In this triangle we know the three sides:

• a = 8,
• b = 6 and
• c = 7.

Use The Law of Cosines (angle version) to find angle C :

Cosine Tables

Versions for a, b and c

Also, we can rewrite the c² = a² + b² − 2ab cos(C) formula into a²= and b²= form.

Here are all three:

a² = b² + c² − 2bc cos(A)

b² = a² + c² − 2ac cos(B)

c² = a² + b² − 2ab cos(C)

But it is easier to remember the 'c²=' form and change the letters as needed !

As in this example:

Example: Find the distance 'z'

The letters are different! But that doesn't matter. We can easily substitute x for a, y for b and z for c

Answer: z = 14.5

Dev C++ Contoh

Did you notice that cos(131º) is negative and this changes the last sign in the calculation to + (plus)? The cosine of an obtuse angle is always negative (see Unit Circle).