SOLUTION: could you please help me with this question If x is in Quadrant IV with cos(x) = 3/5 and y is in Quadrant III with sin(y) = −2/√5, find cos(x+y) I keep on gettin

Algebra.Com
Question 1094865: could you please help me with this question
If x is in Quadrant IV with cos(x) = 3/5 and y is in Quadrant III with sin(y) = −2/√5, find cos(x+y)
I keep on getting -2√5 but that answer is not correct
Found 3 solutions by ikleyn, basharat18, MathTherapy:
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
1.  "x is in Quadrant IV with cos(x) = 3/5"  ====>  sin(x) =  =  = .

    The sign is "-" since sine is negative in QIV.



2.  "y is in Quadrant III with sin(y) = "  ====>  cos(y) =  =  = .

    The sign is "+" since cosine is negative in QIII.



3.  cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) =  =  =  = .


To see more solved similar problems on calculating trig functions, look into the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Trigonometry: Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by basharat18(4)   (Show Source): You can put this solution on YOUR website!
COS (X+Y)= COSXCOSY-SINXSINY;
IF (a,b) be a position vector on xy plane .
sin(angle) = b/sqrroot( a^2 + b^2);
cos (angle)= a/sqrroot(a^2 +b^2);
according to question cosx = 3/5 (base/ hyp);
sinx = -4/5 (iv quad) ;
similarly siny= -2/sqrroot5;(per/hyp)
cosy= -1/sqrroot5;(base/hyp);
now cos(x+y)= (3/5)(-1/sqrroot5)-(-4/5)(-2/sqrroot5);
-11/5sqrroot5;
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
could you please help me with this question
If x is in Quadrant IV with cos(x) = 3/5 and y is in Quadrant III with sin(y) = −2/√5, find cos(x+y)
I keep on getting -2√5 but that answer is not correct
cos (x + y) = cos x cos y - sin x sin y

Q IV

Q III
 ----- Easier to work with a RATIONALIZED denominator
 ------ Easier to work with a RATIONALIZED denominator

cos (x + y) = cos x cos y - sin x sin y



 

RELATED QUESTIONS


suppose sin(x) = 3/5 with x in quadrant I, and cos(y) = 12/13 with y in quadrant IV. find  (answered by lwsshak3)

Find sin (x,y) for tan x= -5/12 and cos = 3/5 with x and y being in Quadrant... (answered by Alan3354)

How do I find sin (x-y) and tan (x+y) if cos x=(-1/3) and tan y= (1/2) with x being a... (answered by lwsshak3)

when sin x= -8/17 and x lies in Quadrant III and cos y= -4/5 and y lies in Quadrant II,... (answered by stanbon)

Find the sin(x) if cos(2x)=2/3, with x terminating in quadrant... (answered by MathLover1)

If sin x = -(4/5) and x is in quadrant IV, find cos (1/2)... (answered by lwsshak3)

if sec x = square root 5/2 with angle x in quadrant IV and tan y= -1/3 with angle y in... (answered by stanbon,Theo)

Find sin (x + y) if sin x = ¾ and cos y = 2/3 with both angles in the first quadrant.
 (answered by josmiceli)

sin x<0 Is it in Quadrant I, Quadrant II, Quadrant III, Quadrant IV, or a Quadrant... (answered by stanbon)