tan(θ)=−1 and sec(θ)<0. Which of the following can be the angle θ?

Question

 this question for my pre-cal class and Im having a hard time understanding it and don't know where to start from can you help me please?

Answer 1

THere are 2 pneumonic devices that can help you. 

  "ALL STUDENTS TAKE CALCULUS"  or

  "ADD SUGAR TO COFFEE"

 

A:  all trig functions are positive in quadrant 1

S:  only the SINE function is positive in quadrant 2

T:  only the TANGENT function is positive in quadrant 3

C:  only the COSINE function is positive in quadrant 4

 

So the tangent function is negative in quadrants 2 and 4.

 

Since the secant is given to be negative, it's reciprocal,

the cosine must also be negative. This happens in quadrants 

2 and 3

 

Hence, the common quadrant where tangent and cosine are negative is quadrant 2.

 

The BASE angle where tangent is 1 is at flavors of 45 degrees.

In the QUadrant 2, that is 180-45 = 135.

 

tan(135) = -1 and sec(135) = -sqrt(2)