SOLUTION: Evaluate the given function with the following information: sin α = 4/5 (α in the first quadrant) and cos β = -12/13 (β in the second quadrant). tan (β –

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate the given function with the following information: sin α = 4/5 (α in the first quadrant) and cos β = -12/13 (β in the second quadrant). tan (β –       Log On


   

Question 1097724: Evaluate the given function with the following information: sin α = 4/5 (α in the first quadrant) and cos β = -12/13 (β in the second quadrant).
tan (β – α)
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  sin%28alpha%29 = 4%2F5  and  alpha  is  in  QI  ====>

    cos%28alpha%29 = sqrt%281-sin%5E2%28alpha%29%29 = sqrt%281-%284%2F5%29%5E2%29 = sqrt%281-16%2F25%29 = sqrt%28%2825-16%29%2F25%29 = sqrt%289%2F25%29 = 3%2F5

    and the sign at sqrt is "+" (positive) since cosine is positive in QI.


    ===============>  tan%28alpha%29 = sin%28alpha%29%2Fcos%28alpha%29 = %28%284%2F5%29%29%2F%28%283%2F5%29%29 = 4%2F3.



2.  cos%28beta%29 = -12%2F13  and  beta  is  in  QII  ====>

    sin%28beta%29 = sqrt%281-cos%5E2%28beta%29%29 = sqrt%281-%28-12%2F13%29%5E2%29 = sqrt%281-144%2F169%29 = sqrt%28%28169-144%29%2F169%29 = sqrt%2825%2F169%29 = 5%2F13

    and the sign at sqrt is "+" (positive) since sine is positive in QII.


    ===============>  tan%28beta%29 = sin%28beta%29%2Fcos%28beta%29 = %28%285%2F13%29%29%2F%28%28-12%2F13%29%29 = -5%2F12.



3.  tan%28beta-alpha%29 = %28tan%28beta%29-tan%28alpha%29%29%2F%281%2Btan%28beta%29%2Atan%28alpha%29%29 = %28%28-5%2F12%29-4%2F3%29%2F%281+%2B+%28-5%2F12%29%2A%284%2F3%29%29 = %28-15%2F36+-+48%2F36%29%2F%281+-+20%2F36%29 = %28%28-63%2F36%29%29%2F%28%2816%2F36%29%29 = -63%2F16.

Answer. tan%28beta-alpha%29 = -63%2F16.

Solved.


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To see many other similar problems, 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.