y = arcsin( cos 48 ); arcsin may be seen as sin-1 on your calculator.
A = arcsin 12
Arcsin
I presume that sin-1x is being used to represent the inverse sin function (I prefer arcsin x to avoid possible confusion). Make use of the trignometirc relationships: cos2θ + sin2θ = 1 ⇒ cosθ = √(1 - sin2θ) cotθ = cosθ/sinθ = √(1 - sin2θ)/sinθ sin(arcsin x) = x Then: cot(arcsin(x)) = √(1 - sin2(arcsin(x))/sin(arcsin(x)) = √(1 - x2)/x ⇒ cot(arcsin(2/3)) = √(1 - (2/3)2)/(2/3) = √(9/32 - 4/32) ÷ 2/3 = √(9 - 4) x 1/3 x 3/2 = 1/2 x √5
Yes, it is called arcsin.
They're the same. They're the same.
sin(arcsin(2/3)) = 2/3, since sin is the inverse function of arcsin.
The integral of arcsin(x) dx is x arcsin(x) + (1-x2)1/2 + C.
arcsin(.75)≈0.848062079
y = arcsin( cos 48 ); arcsin may be seen as sin-1 on your calculator.
arcsin(.75)≈0.848062079
A = arcsin 12
Arcsin
The inverse sin function I write as arcsin x. Make use of the trignometric relationships: cos2θ + sin2θ = 1 ⇒ cosθ = √(1 - sin2θ) cotθ = cosθ/sinθ = √(1 - (sinθ)2)/sinθ sin(arcsin x) = x Then: cot(arcsin(x)) = √(1 - (sin(arcsin(x))2)/sin(arcsin(x)) = √(1 - x2)/x ⇒ cot(arcsin(4/7)) = √(1 - (4/7)2)/(4/7) = √(49/72 - 16/72) ÷ 4/7 = √(49 - 16) x 1/7 x 7/4 = 1/4 x √33
NO FALSE
( are you in radians, or degree mode? will do both) Radians: sin C = 0.3328 arcsin(0.3328) = C =0.3393 radians --------------------- Degrees: sin C = 0.3328 arcsin(0.3328) = 19.44 degrees ------------------------- arcsin is a secondary function on most calculators and you should recognize the algebraic/trig manipulations.
arcsin(0.329) = 0.335 radians = 19.21 degrees