Evaluate without using a calculator by using ratios in a reference triangle.

cos 5pi/3

The answer is 1 / 2

Step-by-step explanation:

Cos, tan and sin are all positive in the first quadrant, but depends on the direction of the angle. Reference angle here we are looking for is the one in relation to the quadrant cos 5pi/3.

Any multiples of cos outside 2nd quadrant will give a positive value.

cos 5pi/3 is located in the 4th quadrant, while, cos pi/3 is located in the 1st quadrant, where the cos ratio has a positive value.

In terms of cosine, anytime the angle falls on the first or fourth quadrant it will always produce a positive graph.

For cos 5pi/3, cos pi/3 and cos 7pi/3 will give the same answer as "1/2" or "0.5" because, cos pi/3 will give 60 degrees which fall in the first quadrant

If "R" is a real number, for all R multiplied by pi/3, the new value gives an angle in the first or fourth quadrant, the angle will be 0.5

The exact value of cos 5 (π / 3) is 1 / 2.