Find an exact solution to the equation below so that 0 < t < pi.?

Question

http://www.webassign.net/www22/symImages/b/d/6e5329bc36ec3482f2fafe63228196.gif

1 + tan (t)

----------------- = 0

sin (t)

Answer 1

The denominator does not play into the answer for two reasons: 1) both sides of the equation can be multiplied by sin(t) and the sin(t) term is removed, 2) the numerator has to be the point on the circle where the tan = -1.

There are only two places on the circle between 0 and pi where the sin and cos are equal and that is required since the tan = sin/cos.  Those two places are at pi/4 and 3pi/4.

At pi/4 the sin and cos are both equal to SQRT(2)/2 which results in a numertor of 2 which does not result in a zero answer.

At 3pi/4 the sin is SQRT(2)/2 and the cos is -SQRT(2)/2.

Therefore, the exact solution is 3pi/4 or 135 degrees.

Hope that helps!