Find the value of each of the six trignometric functions of

Find the value of each of the six trignometric functions of the angle theta in the figure. Sin theta = cos theta = tan theta = csc theta = sec theta = cot theta =

Solution

let the unknown side be \'c\'

by the law of cosines generalizes the Pythagorean theorem

c^2 = a^2 +b^2

given a=24, b=10

c^2 = (24)^2 +(10)^2

c^2 = 576 +10

c^2 =676

c=26

now we know all sides

sin = opposite side/ hypotenuse

sin = b/c

sin = 10/26

sin =5/13

cos = adjacent side /hypotenuse

cos =a/c

cos =24/26

cos =12/13

tan = opposite side/adjacent side

tan = 5/12

csc = 1/sin

csc = 13/5

sec =1/cos

sec = 12/13

cot =1/tan

cot =12/5