Trig Homework help!!?

Question

Without using a calculator, use the properties of inverse functions to find the exact value of the expression.

sin(arcsin 0.7)

i don't just need the answer, can you help expalain it as well? thanks

Answer 1

sin(x) is a ratio that the angle x makes between the opposite and the hypontenuse.

arcsin(x) is an angle that the ratio x makes when that angle is evualted as the sin(x) funtion.

So when you take the sin(arcsin(x)) you are saying give me the ratio of the angle,sin(), but that angle, arcsin(x), is the angle made when the sin = x. Well, that that's like going in a circle, the raito of the angle that is the angle when the ratio is x.

So the value of sin(arcsin(0.7)) is the value of the ratio that is found with the angle that is arcsin(0.7) is evaluated. arcsin(0.7) is the angle formed when the sin of that angle is 0.7. So to evaluate that with the sin it give it right back, that is the ratio!

Answer 2

Basically, the function of the inverse function is the value of the number in the inverse function. So the value is 0.7.

Answer 3

sin(arcsin 0.7) = 0.7

Sin and arcsin are opposites. They just cancel each other.

Answer 4

sin(sin^-1(x)) = x

to understand this

let arcsin(0.7) = x -> by definition sin x = 0.7

so sin(arcsin(0.7)) = sinx = 0.7

Answer 5

Its 0.7 (arscin)

Answer 6

it somewhat is a trigonometric identification, actual shown via construction a suitable triangle and employing the definition of the trigonometric purposes cos(x)=sin(ninety-x) and cos(ninety-y)=sin(y), presented x and y are measured in ranges So sin(38)=cos(fifty two)