Question

find the exact values of sectheta=-2

Answer 1

If the question is asking for theta, we want to find out whatever exact values of theta will give us -2.

Recall that the sec(x)=1/cos(O)

So really, we want the values of theta that make cos(O)=-1/2



Remember the unit circle. For what values of O is the point 1/2 a unit away from the y axis in the negative direction? 5pi/6 and 7pi/6 is the answer.

Also, any co-terminal angles will work. If the problem asked you to find all values of theta that work, you will need to add 2pi*n to both answers, because there are an infinite number of angles who have secants of -2.