Answer:
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)
Step-by-step explanation:
