evaluate: cos(arcsin(5/13)) without a calculator, please explain?
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As always in math, work from the inside out.
arcsin(5/13) = x, means sin(x) = 5/13
sin(x) = o/h, so opposite = 5, hypotenuse = 13
1) draw a right triangle with angle(x), hypotenuse 13, and opposite leg 5
2) use Pythagorean Theorem to find missing leg
You have a 5-12-13 triangle.
3) cos(x) = a/h
cos(x) = 12/13
cos(arcsin(5/13)) = 12/13
arcsin(5/13) = x, means sin(x) = 5/13
sin(x) = o/h, so opposite = 5, hypotenuse = 13
1) draw a right triangle with angle(x), hypotenuse 13, and opposite leg 5
2) use Pythagorean Theorem to find missing leg
You have a 5-12-13 triangle.
3) cos(x) = a/h
cos(x) = 12/13
cos(arcsin(5/13)) = 12/13