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 ->  Trigonometry-basics -> 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      Log On


   



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(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  "x is in Quadrant IV with cos(x) = 3/5"  ====>  sin(x) = sqrt%281-cos%5E2%28x%29%29 = sqrt%281-%283%2F5%29%5E2%29 = -4%2F5.

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



2.  "y is in Quadrant III with sin(y) = -2%2Fsqrt%285%29"  ====>  cos(y) = sqrt%281-sin%5E2%28y%29%29 = sqrt%281-4%2F5%29 = -1%2Fsqrt%285%29.

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



3.  cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) = %283%2F5%29%2A%28-1%2Fsqrt%285%29%29+-+%28-4%2F5%29%2A%28-2%2Fsqrt%285%29%29 = -3%2F%285%2Asqrt%285%29%29+-+8%2F%285%2Asqrt%285%29%29 = -11%2F%285%2Asqrt%285%29%29 = -11sqrt%285%29%2F25.


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) About Me  (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) About Me  (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
matrix%281%2C3%2C+cos+%28x%29%2C+%22=%22%2C+3%2F5%29
matrix%281%2C3%2C+sin+%28x%29%2C+%22=%22%2C+-+4%2F5%29

Q III
 ----- Easier to work with a RATIONALIZED denominator
matrix%281%2C5%2C+cos+%28y%29%2C+%22=%22%2C+-+1%2Fsqrt%285%29%2C+or%2C+-+sqrt%285%29%2F5%29 ------ Easier to work with a RATIONALIZED denominator

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