Question

Help with trig Identities

Answer 1

\[\tan \theta= -2 and \sin \theta<0, find \sec \theta \]

Answer 2

ok... so

\[\tan(\theta) = -2\]

and

\[\sin(\theta) < 0\]

so which quadrant of the unit circle has both sin and tan negative

Answer 3

three?

Answer 4

tan=sin/cos=negative in this case
if we know sin=negative
then cos is ?

Answer 5

recall
(-)/(-)=+
(-)/(+)=-
(+)/(-)=-
(+)/(+)=+

Answer 6

we can only consider the two middle ones there since our quotient is negative
(-)/(+)=-
(+)/(-)=-

Answer 7

positiive if two are negatives

Answer 8

and we know sin is neg
so we have (-)/(+)=-

Answer 9

but we are given tan is negative not positive

Answer 10

-=-/+

Answer 11

so cosine has to be positive right?