Question

Find the exact value o (a) sin(sin^(-1).7)

Answer 1

The exact value of sin(sin^(-1)(0.7)) is 0.6947.

Explanation:

To find the value of sin(sin^(-1)(0.7)), we can use the inverse trigonometric function to find the angle whose sine is 0.7, and then take the sine of that angle.

Let's denote the angle whose sine is 0.7 as x.

So sin(x) = 0.7.

To find x, we can use the arcsine function (sin^(-1)).

Therefore, x = sin^(-1)(0.7).

We can use a calculator to find the approximate value of x.

Using a calculator, we find that x ≈ 0.7754 radians.

Now, we can find the value of sin(x) using the sine function.

So sin(0.7754) ≈ 0.6947.

Therefore,

The exact value of sin(sin^(-1)(0.7)) is approximately 0.6947.