SOLUTION: Find the exact value for cos(alpha+beta) if sin(alpha) = -3/5 and sin(beta) = 5/13 with alpha in quadrant 3 and beta in quadrant 1 Thank you smart people

Question 1099718: Find the exact value for cos(alpha+beta) if sin(alpha) = -3/5 and sin(beta) = 5/13 with alpha in quadrant 3 and beta in quadrant 1
Thank you smart people
Found 3 solutions by Fombitz, MathTherapy, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

and

So then,

Since is in Q3, cosine is negative so,

and similarly,

Since is in Q1, cosine is positive so,

So putting it all together,

Work through that to get the answer.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Find the exact value for cos(alpha+beta) if sin(alpha) = -3/5 and sin(beta) = 5/13 with alpha in quadrant 3 and beta in quadrant 1
Thank you smart people

, with in QIII
As the above is a 3-4-5 PYTHAG. TRIPLE, we get: A = - 4, and so:
, with β in QI
As the above is a 5-12-13 PYTHAG. TRIPLE, we get: A = 12, and so:

Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.
For many other similar solved problems on calculating trig functions see 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.

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