Question

if sin(theta)sec(theta) = -1 and theta lies in second quadrant ,find sin theta and sec theta

Answer 1

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

look at the `Reciprocal Identities` section (page 2) and you'll see that \[\Large \sec(\theta) = \frac{1}{\cos(\theta)}\]

Answer 2

also look in the `Tangent and Cotangent Identities` section just above the reciprocal section and you'll see
\[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]

Answer 3

Doing all this will hopefully convince you that
\[\Large \sin(\theta)\sec(\theta) = -1\]
is the same as
\[\Large \tan(\theta) = -1\]

Answer 4

okay,
what next?

Answer 5

Then tan theta = -1/1

Answer 6

Draw an xy axis

Answer 7

we're in quadrant 2 now