Question 1042627
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Given sin(A) = 6/7 and cos(B) = -1/6, where A is in quadrant II and B is in quadrant III, find sin(A+B), cos(A-B), and tan(A-b)
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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Calculating-trigonometric-functions-of-angles.lesson>Calculating trigonometric functions of angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Selected-problems-from-the-archive-on-calculating-trig-functions-of-angles.lesson>Advanced problems on calculating trigonometric functions of angles</A>

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<pre>
The instructions are as follows:

1.  Knowing that sin(A) = {{{6/7}}}, calculate cos(A) = +/- {{{sqrt(1-sin^2(A))}}}.

2.  Knowing that the angle A is in QII, determine the sign at the square root in the n.1 above.

3.  Knowing that cos(B) = {{{-1/6}}}, calculate sin(B) = +/- {{{sqrt(1-cos^2(B))}}}.

4.  Knowing that the angle B is in QIII, determine the sign at the square root in the n.3 above.


5.  As a last step, apply the formulas 

       sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B),

       cos(A-B) = cos(A)*cos(B) + sin(A)*sin(B).

       tan(A-B) = {{{(tan(A) + tan(B))/(1-tan(A)*tan(B))}}}.


Notice that you just have everything to substitute into these formulas.
</pre>

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&nbsp;&nbsp;&nbsp; -&nbsp;<A HREF = http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A>

&nbsp;&nbsp;&nbsp;&nbsp; - <A HREF = http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas-Examples.lesson>Addition and subtraction formulas - Examples</A>

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