find the value of sin(cos-1(-1/sqrt6))?

Question

im having troubles finding the value of this function WITHOUT USING A CALCULATOR sin(cos-1(-1/sqrt6))
thanks to all that help

Answer 1

First use a basic principle of the cosine function.

cos^-1[-1/sqrt(6)] = pi - cos^-1[1/sqrt(6)]

Now take the sine

sin(pi - cos^-1[1/sqrt(6)])

And use the relation sin(pi + x) = -sin(x) to get

sin(-cos^-1[1/sqrt(6)]) = -sin(cos^-1[1/sqrt(6)])

Finally use the relation that sin(arccos(x)) = sqrt(1-x^2)

and

-sin(cos^-1[1/sqrt(6)]) = -sqrt(1-1/6) = -sqrt(5/6)

At least I think I did that correctly.

Answer 2

Let A be the angle whose cosine is -1/sqrt6

We want to find sinA

But we know that sin^2(A) + cos^2(A) = 1

We also know, from the given, that cosA = -1/sqrt6

Therefore sin^2(A) + (-1/sqrt6)^2 = 1
sin^2(A) + 1/6 = 1
sin^2(A) = 5/6

We have 2 answers:
sinA = +sqrt(5/6)
and sinA = -sqrt(5/6)

Answer 3

Let a = cos-1(-1/sqrt(6)). Then, cos a = -1/sqrt(6) and sin^2(a) = 1 - cos^2(a) = 1 - (-1/sqrt(6))^2 = 1 -1/6 = 5/6.

Since cos(a) < 0, a is in the 3rd or the 4th quadrant. Anyway, we have 2 possibilities for sin(a)

sin(a) = sqrt(5/6) or b sin(a) = - sqrt(5/6).

Based only on the fact that cos(a) = - 1/sqrt(6), it's not possible to determine sin(a). We must know if a is in the 3rd - in which case sin(a) = sqrt(5/6) - or in 4 rd - in which case sin(a) =- sqrt(5/6) - quadrant.

Answer 4

Do the inverse cos function then draw a triangle and do the sign of the triangle

Answer 5

i visit piggy economic company them if i'm close to my piggy. If not I completely trash them to be ordinary. Pennys at the instant are not well worth a concern now a days. until you keep greater beneficial than a hundred of them....and who's typical with how long which will take.

Answer 6

the awnser is 3 x i think