aWrite sint in terms of cost Sint in quadrant III b Write ta

a)Write sin(t) in terms of cos(t)   Sin(t) in quadrant -III

b) Write tan(t) in terms of sec(t) :tan(t) in quadrant IV   

Solution

sin² t + cos²t=1

sin²t=1-cos²t

sint= +-sqrt(1-cos²t)

and in third quadrant sin theta is negative

sin t=-sqrt(1-cos²t)

b. sec²t-tan²t=1

tan²t= sec²t -1

tan t= +-sqrt(sec²t-1)

In third quadrant tan theta is positive

Therefore tan t= sqrt(sec²t-1)