Find the value of sin t given that sect 3 and tan t 0 Expr

Find the value of sin t given that sect = 3 and tan t > 0. Express your answer as a simplified radical. (Don\'t use your calculator. You must SHOW all the correct algebraic steps for credit. No decimals!).

Solution

sec t = -3 , tan t > 0 , it means angle is in 3rd Quadrant as tan t is positive in 3rd Quadrant.

Cos t = 1/sec t = -1/3

Now, sin²t + cos²t = 1

=> sin²t = 1- cos²t = 1 - (-1/3)² = 1- 1/9 = 8/9

sint = (8/9)^1/2 = +22/3 or -22/3

Since, angle lies in 3rd quadrant. So sin t will be negative.

Hence, sin t = -22/3