Sorry for the picture being sideways but I need help with 47

Sorry for the picture being sideways, but I need help with #47 and #51(does not have a picture but has x and y coordinates)

For #47: Given (x,y) is a point on a unit circle corresponding to t, find the value of all six circular functions of t.

#51: Given (x,y) is a point on a unit circle corresponding to t, find the value of all six circular functions of t.

(-2/5 , sqrt21/5)

Solution

# 47 ) (x,y) = (-5/13, -12/13)

According to the unit circle formula,

Sin t = y ; Cos t = x

Calculating the same we get

Sin t = (-12/13)
Cos t = (-5/13)
Tan t = (Sin t / Cos t) = 12/5
Cosec t = (1 / Sin t) = (-13/12)
Sec t = (1 / Cos t) = (-13/5)
Cot t = (1 / Tan t) = 5/12

#51) (x,y) = (-2/5, sqrt21/5)

According to the unit circle formula,

Sin t = y ; Cos t = x

Calculating the same we get

Sin t = sqrt21/5
Cos t = (-2/5)
Tan t = (Sin t / Cos t) = (-sqrt21/2)
Cosec t = (1 / Sin t) = 5/sqrt21
Sec t = (1 / Cos t) = (-5/2)
Cot t = (1 / Tan t) = (-2/sqrt21)