If csc theta 2524 90 less than or equal to theta less than

If csc (theta) = 25/24, 90 less than or equal to theta less than or equal to 180, then the exact value of Sin (theta0 equals cos (theata) equals tan (theta) equals

Solution

csc =25/24

90<=<=180

csc=hypotenuse/oppositeside

by pythogorus theorem

hypotenuse²=oppositeside²+adjacentside²

25²=24²+adjacentside²

adjacentside²=625-576

adjacentside=7

sine is positive in 90<=<=180

sin=oppositeside/hypotenuse

sin=24/25

cos is negative  90<=<=180

cos=-adjacentside/hypotenuse

cos=-7/25

tan is negative  90<=<=180

tan=-oppositeside/adjacentside

tan=-24/7