Question 1161053
One of the primary trigonometric ratios for an angle is given, as well as the quadrant that the terminal arm lies in. Determine the other two primary trigonometric ratios. 
a) sin A = 4/5, first quadrant 
b) cos B = 8/17, fourth quadrant 
c) tan C = -12/5, second quadrant 
<pre>The 3 primary TRIG. RATIOS are sin, cos, and tan
<b>a)</b> {{{matrix(1,7, sin (A), "=", O/H, "=", 4/5, "=", y/r)}}}
   This represents one of the many PYTHAGOREAN TRIPLES, as this is a 3-4-5 right triangle.
   And, with &#8737A being in the 1st quadrant, where ALL RATIOS are POSITIVE (+), and y being 4, r being 5, we get "x" to be 3.
   The other 2 TRIG. RATIOS are: {{{highlight_green(matrix(2,7, cos (A), "=", A/H, "=", x/r, "=", 3/5, tan (A), "=", O/A, "=", y/x, "=", 4/3))}}}
<b>b)</b> Let me GUIDE you!
   {{{matrix(1,7, cos (B), "=", A/H, "=", 8/17, "=", x/r)}}}
   This represents one of the many PYTHAGOREAN TRIPLES, as this is an 8-15-17 right triangle.
   And, with &#8737B being in the 4th quadrant, where ONLY "cos" is POSITIVE (+), and x being 8, r being 17, we get "y" to be - 15.
   The other 2 TRIG. RATIOS are: {{{highlight_green(matrix(2,7, sin (B), "=", O/H, "=", y/r, "=", "?"/"?", tan (B), "=", O/A, "=", y/x, "=", "?"/"?"))}}} <b><======= Fill in the MISSING pieces!</b>
<b>c)</b> Let me GUIDE you!
   {{{matrix(1,7, tan (C), "=", O/A, "=", 12/(- 5), "=", y/x)}}}
   This represents one of the many PYTHAGOREAN TRIPLES, as this is a 5-12-13 right triangle.
   And, with &#8737C being in the 2nd quadrant, where ONLY "sin" is POSITIVE (+), and x being - 5, y being 12, we get "r" to be 13.
   The other 2 TRIG. RATIOS are: {{{highlight_green(matrix(2,7, sin (C), "=", O/H, "=", y/r, "=", "?"/"?", cos (C), "=", A/H, "=", x/r, "=", "?"/"?"))}}} <b><======= Fill in the MISSING pieces!</b>