Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.
Expand the tan expression using the angle sum identities for sin and cos :
tan(u + v) = sin(u + v) / cos(u + v)
tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]
Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.
Recall that for all x,
cos²(x) + sin²(x) = 1
and it follows that
cos(u) = - √(1 - sin²(u)) = -12/13
sin(v) = - √(1 - cos²(v)) = -3/5
Then putting everything together, we have
tan(u + v)
= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]
= 56/33
(or, if sin(u) = -12/13, then tan(u + v) = -63/16)
To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.
Then we need to make 7 parts of each circle.
For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.
For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.
So, the first circle represents 2:7 ratio and second circle represents 5:7 ratio.
Sunday will be twice her age in 2038. Hope this helps
17 10$ coins.
19 20$ coins.
Hope this helped☺☺