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Sin A = 336/ 625 where 450 degree

Grade:11

1 Answers

Shankar
20 Points
one year ago
If 450°
So A is in the second quadrant.
so cos A = -√(1 - (336/625)²) = -527/625

I like tan(x/2) = (1 - cos(x))/sin(x) because it has no radicals in it.

tan(A/2) = (1 + 527/625)/(336/625) = 24/7

If 450°

A reference triangle for A/2 would then be y = -24, x = -7, r = 25

So cos(A/2) = -7/25 and sin(A/2) = -24/25

Then tan(A/4) = (1 - cos(A/2))/sin(A/2) = (1 + 7/25)/(-24/25) = -4/3

If 450°

A reference triangle for A/2 would then be y = 4, x = -3, r = 5

So sin(A/4) = 4/5

CHECK
We note that arcsin(336/625) = 0.5675882184 radians = 32.52040941662392°
which is in the first quadrant.
Subtract it from 180° and we get 147.47959058337608
which is in the second quadrant.
Add 360° and we get A = 507.4795905833761°

So sin(A/4) comes out 0.8 = 4/5

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