Cos Formula

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Cos formula is an effective tool in trigonometric functions.  Cos formula is based on right angle triangle. In right angle triangle with legs a, b and c and angle k is opposite to side a, the cos angle k is defined as length of adjacent side divide by length of hypotenuse.


In simple cos (A) = adjacent / hypotenuse
The following examples illustrates the use of cos formula
Example 1: If X = 16, Y = 30, and Z = 34, what is the cos of A?



Solution: In the right triangle, the cosine of A is the ratio of the side adjacent A to the hypotenuse.
=> Cos (A) = adjacent / hypotenuse
=> Cos (A) = X / Z
=> Cos (A) = 16 / 34 = 0.471
=> Therefore cos (A) = 0.471.
 
 Example 2: Find the size of a0?


Solution: From the figure we know
=> Length of adjacent side = 6750
=> Length of hypotenuse = 8100
=> Use cos formula: Cos (a) = adjacent / hypotenuse
=> So, cos (a) = 6750/8100 = 0.83333
=> Find the angle using calculator cos^-1(0.83333)
=> cos^-1(0.83333) = 33.6


Example 3: Find the length of x in the below figure?


Solution: In figure it is shown that the angle is 60 degrees.
=> The hypotenuse is given as 13cm and we need to find the adjacent side. This formula that connects angle, hypotenuse and adjacent side is cos formula.
 
=> We know that Cos (angle) = adjacent side / hypotenuse

=> Therefore, cos (60) = x / 13
 
=> We know that Cos (60) = ½ = 0.5
 
=> So, x = 13 × cos (60) = 13 x 0.5 = 6.5

=> Hence, the length of   x = 6.5cm


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