SOLUTION: if sinq is negative and cosq is negative in which quadrant does the terminal side q lie?

Question 720779: if sinq is negative and cosq is negative in which quadrant does the terminal side q lie?

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Remember the sentence "ALL STUDENTS TAKE CALCULUS" to remember the
letters A,S,T,C for these words: 

1. the word ALL
2. the word SINE
3. the word TANGENT
4. the word COSINE

This works for the basic three trig functions SINE, COSINE, TANGENT.

Quadrant I:   A for ALL three of the basic three trig functions are positive
              in quadrant I which is 0 < q < 90� if q is measured in degrees 
              or 0 < q <  if q is measured in radians.


Quadrant II:  S for the SINE is positive and the other two basic trig functions
              are negative in quadrant II which is 90� < q < 180� if q is 
              measured in degrees or < q < p if q is measured in radians.

Quadrant III: T for the TANGENT is positive and the other two basic trig functions
              are negative in quadrant III which is 180� < q < 270� if q is 
              measured in degrees or p < q <  if q is measured in radians.

Quadrant IV:  C for the COSINE is positive and the other two basic trig functions
              are negative in quadrant IV which is 270� < q < 360� if q is 
              measured in degrees or < q < 2p if q is measured in radians.

The above scheme tells you what signs the three basic trig functions SINE,
COSINE, and TANGENT have in the various quadrants.  It does not work for
SECANT, COSECANT and COTANGENT, so don't mistake the S and C from "ALL
STUDENTS TAKE CALCULUS" for those, but only for SINR and COSINE.  The way to
remember the signs of the SECANT, COSECANT, and COTANGENT, is to remember that
the SECANT is the reciprocal of the COSINE and the SECANT will have the same
sign as the COSINE. The same for the other two reciprocal functions.  The
COSECANT is the reciprocal of the SINE and the COSECANT will have the same
sign as the SINE. The COTANGENT is the reciprocal of the TANGENT and the
COTANGENT will have the same sign as the TANGENT.

Your question is:

if sinq is negative and cosq is negative in which quadrant does the terminal side q lie?


Think of the sentence "ALL STUDENTS TAKE CALCULUS".  The SINE is positive
in quadrants I and II and negative in quadrants III and IV.  So the answer
is either quadrant III or IV.  The cosine is positive in quadrants I and IV,
and negative in quadrants II and III, so that eliminates quadrant IV, and so
the answer is quadrant III.

Edwin

RELATED QUESTIONS
If cotq = -3/4 and sinq < 0,... (answered by AnlytcPhil)

Find the minimum value of cosq + 2sin (answered by Edwin McCravy)

cosq = 5/12 and tanq is (answered by AnlytcPhil)
Find the exact value of sin(2q) if csc( (answered by stanbon,Edwin McCravy)
Show that the equation below is NOT an identity. � (answered by Edwin McCravy)
This is a trignometry problem on proving identities I can use:double-angle,sum and... (answered by Edwin McCravy)
how do you Verify this equation?: sin(np + (answered by Edwin McCravy)
Name the quadrants in which angle theta may lie if sec(q) =... (answered by Edwin McCravy)

Let a and b be acute... (answered by AnlytcPhil)

SOLUTION: if sin<font face="symbol">q</font> is negative and cos<font face="symbol">q</font> is negative in which quadrant does the terminal side <font face="symbol">q</font> lie?