SOLUTION: A) If sinA=-1/25 and angle A terminates in quadrant IV, what does tanA equal? B) Given tan theta=7/24, and theta terminates in Quadrant III, determine the value of cos theta.

Algebra ->  Trigonometry-basics -> SOLUTION: A) If sinA=-1/25 and angle A terminates in quadrant IV, what does tanA equal? B) Given tan theta=7/24, and theta terminates in Quadrant III, determine the value of cos theta.       Log On


   

Question 1160460: A) If sinA=-1/25 and angle A terminates in quadrant IV, what does tanA equal?
B) Given tan theta=7/24, and theta terminates in Quadrant III, determine the value of cos theta.
C) If sin theta= 1/2 and theta terminates in Quadrant II, what is the valuse of csc theta * cot theta?
Found 3 solutions by Theo, MathLover1, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if the angle is in the first quadrant then all the trig functions will be positive.
the reference angle is always in the first quadrant.
solve for the positive value of the trig function and you have the reference angle.
you can then determine what quadrant it belongs in by either the sign of the trig function or being told what quadrant it's in.

A.
arcsin(1/25) = 2.292442776 degrees.
the sine function is negative in quadrants 3 and 4.
you are told the angle is in quadrant 4.
the angle in quadrant 4 is equal to 360 minus the reference angle.
that makes the angle 360 - 2.292442776 = 357.7075572 degrees.

B.
tan(theta) = 7/24 and theta terminates in quadrant 3.
the tan function is positive in quadrants 1 and 3.
you are told the angle is in quadrant 3.
arctan(7/24) = 16.26020471 degrees.
the angle in quadrant 3 is equal to 180 plus the reference.
that makes the angle 180 + 16.26020471 = 196.26020471 degees.
degrees.

C.
sin(theta) = 1/2 and theta terminates in quadrant 2.
determine the value of csc(theta) * cot(theta).
arcsin(1/2) = 30 degrees.
that's in quadrant 1 and that's the reference angle.
theta terminates in quadrant 2.
the angle in quadrant 2 is equal to 180 minus the reference angle.
that makes the angle equal to 180 - 30 = 150 degrees.
tan(150) = -.5773502692.
you have, so far.
sin(150) = 1/2
tan(150) = -.5773502692.
csc(150) = 1/sin(150) = 1/(1/2) = 2
cot(150) = 1/-.5773502692 = -1.732050808.
csc(150) * cot(150) = 2 * -1.732050808 = -3.464101615














Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A)
If sin%28A%29=-1%2F25+and angle+A terminates in quadrant IV, what does tan%28A%29 equal?
If sin%28A%29=-1%2F25+

since sin%28A%29=opposite%2Fhypotenuse=>opposite=1 and hypotenuse=25
to find tan%28A%29 , we need cos%28A%29=adjacent%2Fhypotenuse
and adjacent=sqrt%2825%5E2-1%5E2%29=sqrt%28624%29=4sqrt%2839%29
cos%28A%29=adjacent%2Fhypotenuse
cos%28A%29=4sqrt%2839%29%2F25

then tan%28A%29=sin%28A%29%2Fcos%28A%29

tan%28A%29=%28-1%2F25%29%2F%284sqrt%2839%29%2F25%29......simplify
tan%28A%29=-1%2F%284sqrt%2839%29%29
tan%28A%29=-sqrt%2839%29%2F%284%2A39%29
tan%28A%29=-sqrt%2839%29%2F156 in radians

A=-2.29241°

in quadrant IV: A=360-2.29241=357.70759°


B) Given tan%28+theta%29=7%2F24, and+theta terminates in Quadrant III, determine the value of cos+theta.
tan%28A%29=sin%28A%29%2Fcos%28A%29=opposite%2Fadjacent=> opposite=7 and adjacent=24
find hypotenuse
hypotenuse=sqrt%287%5E2%2B24%5E2%29
hypotenuse=sqrt%28625%29
hypotenuse=±25

since +theta terminates in Quadrant III, cos%28A%29 is negative
so, hypotenuse=-25
cos%28A%29=24%2F-25

cos%28A%29=-24%2F25
since tan%28theta%29+=+7%2F24, use your calculator to find theta+=+16.26°
that's in the first quadrant
in the third quadrant, the angle is 180+%2B+16.26° = 196.26°
so,
A=196.26°


C)
If sin%28theta%29=+1%2F2 and theta terminates in Quadrant II, what is the values of csc%28theta%29%2Acot%28theta%29?

in Quadrant II: sin is positive, cos is negative, tanis negative
sin%28A%29=opposite%2Fhypotenuse=>opposite=1 and hypotenuse=2
and adjacent=sqrt%282%5E2-1%5E2%29=sqrt%283%29

then cos%28A%29=-sqrt%283%29%2F2

since csc%28theta%29+=hypotenuse%2Fopposite we have

csc%28theta%29+=2%2F1=2

cot%28theta%29+=+adjacent%2Fopposite

cot%28theta%29+=+sqrt%283%29%2F1

cot%28theta%29+=+sqrt%283%29+

then
csc%28theta%29+%2A+cot%28+theta%29=2sqrt%283%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A) If sinA=-1/25 and angle A terminates in quadrant IV, what does tanA equal?
B) Given tan theta=7/24, and theta terminates in Quadrant III, determine the value of cos theta.
C) If sin theta= 1/2 and theta terminates in Quadrant II, what is the valuse of csc theta * cot theta? 
I'll only do A) for you, and none of these are done the way the other 2 RESPONDENTS state. 

While NOT requested, answers of these forms are generally EXACT!

With ∡A being in Q IV, we get: 

                               

That's how SIMPLE A) is!!