SOLUTION: Let cosA=-5/13 with A in Q3 and sinB=3/5 with B in Q1. Find sin(A-B), cos(A-B), and tan(A-B). All I know how so far is just the formula sin(A-B)=sinAcosB-cosAsinB and cos(A-B)=c

Question 1162379: Let cosA=-5/13 with A in Q3 and sinB=3/5 with B in Q1. Find sin(A-B), cos(A-B), and tan(A-B).
All I know how so far is just the formula sin(A-B)=sinAcosB-cosAsinB and cos(A-B)=cosAcosB+sinAsinB.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

5-12-13 and 3-4-5 are Pythagorean Triples.

Given cosA = -5/12, sinA is 12/13 or -12/13, depending on the quadrant.

Given sinB = 3/5, cosB is 4/5 or -4/5, depending on the quadrant.

After you find sinA and cosB, use the formulas you show to find sin(A-B) and cos(A-B).

Then tan(A-B) is just sin(A-B) divided by cos(A-B).

Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

For many similar solved problems (your TEMPLATES) see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions
in this site.

Learn from there as much as you can (!) (!)

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.

RELATED QUESTIONS
let sinA= 3/5 with A in Q1 and sinB= -5/13 with b in quadrant 3. find sin(A+B), cos(a+b), (answered by Solver92311)
find the exact values of sin(A+B), cos(A+B), and tan(A+B), given: a.) sin A = 8/17,... (answered by Edwin McCravy)
let sinA= 3/5 with A in Q2 and sinB= -5/13 with b in quadrant 3. find sin(A+B), cos(a+b), (answered by ikleyn)
let cos A = -5/13 with A in Q2 and sin B= 3/5 with B in Q1 Find 1. CSC(A-B) 2.... (answered by lwsshak3)
Given: cos A = 3/5, tan B = 12/5, A is in Q1 and is in Q3 Find Sin (A +... (answered by ikleyn)
Given that sin A= -4/5 where A is in quadrant 3 and sin B= 12/13 where B is in quadrant... (answered by lwsshak3)
cos a = 4/9, a in Q1, and tan b = -5/4, b in Q2. Find sin (a+b), cos (a+b), tan... (answered by Alan3354,KMST)
sin a = 3/5, cos b = 15/17, a and b in Q1 Find sin ( a+b ), cos (a+b) (answered by Alan3354)
\cos A=\frac{5}{13}cosA= 13 5 and \sin B=\frac{12}{37}.sinB= 37 12  (answered by ikleyn)