Let theta be an angle in quadrant III such that sin theta 3

Let theta be an angle in quadrant III such that sin theta = -3/5. Find the exact values of sec theta and tan theta.

Solution

given

sin(theta0 = - 3/5

if it is in quadrant 3 then the cos is also negative.
draw a triangle you\'ll see 5 is your hypotenuse and -3 is your y-value.
pythagorean theroem.

a^2+b^2=c^2

(-3)^2+b^2=5^2

9+b^2=25

b^2=16

b=-4 or 4.

since cos has to be negative then b=-4.

now find cos first which is -4/5 then secx=-5/4

tanx=-3/4.