Calculate the value of each of the trigonometric functions if: cosa = 5/12

cosa = 5/12, and belongs to the first quarter.

Let us express the sine of the angle from the formula 1 = sin ^ 2a + cos ^ 2a.

sin ^ 2a = 1 – cos ^ 2a.

Let’s calculate the sine value: sin ^ 2a = 1 – (5/12) ^ 2 = 1 – 25/144 = 144/144 – 25/144 = 119/144.

sina = √ (119/144) = √119 / 12.

The formula for finding the tangent of an angle is tga = sina / cosa.

Let’s calculate the value of the tangent:

tga = √119 / 12: 5/12 = √119 / 12 * 12/5 = √119 / 5.

So the cotangent and tangent are inverse functions, that is, ctga = 1 / tga, which means:

ctga = 5 / √119.

Answer: sina = √119 / 12, tga = √119 / 5, ctga = 5 / √119.