Picture attached given that tan 0=-1, what is the value of sec0 for 3pi/202pi?

   = -sqrt(2)

Step-by-step explanation:

tan theta = -1

we know tan = opposite/ adjacent

So opposite/adjacent = -1

Multiply by adjacent on each side

opposite = - adjacent

We also know from pythagorean theorem that

opposite ^2 + adjacent ^2 = hypotenuse ^2

Substituting in for adjacent

opposite ^2 + (-opposite ) ^2 = hypotenuse ^2

opposite ^2 + opposite ^2 = hypotenuse ^2

2 opposite ^2 = hypotenuse ^2

 Taking the square root on each side

sqrt(2 opposite ^2)   =  sqrt(hypotenuse ^2)

sqrt(2) opposite = hypotenuse

We are now set to find the sec

sec theta = hypotenuse / adjacent

               = sqrt(2) opposite/ adjacent

Replace the opposite = -adjacent

                 = sqrt(2) (-adjacent)/adjacent)

                 = -sqrt(2)