Find the approximate value of s, to four decimal places, in th...

Question

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

sin s = 0.4924

Accepted Answer

Welcome back everyone. In this problem considering the interval, open bracket, zero half of pi close bracket. We want to find the approximate value of X and we want to round our answer to four decimal places. Our equation is the sin of X equals 0.8973. And for our answer choices, A is 0.4572. B is 1.1136 C is 0.1136 and D is 1.4572. Now essentially we're trying to solve for X in an equation to help us solve. It would be good. It would be good for us to think about the nature of our equation. So we're talking about the sine function. How does a function work? Well, recall that in a function, OK, we take an input value, put it into our function. In this case. S and we get an output value in this case or a result of 0.8973. So to figure out what value was our input, we can do the inverse, we can use the inverse function of S the inverse function of sine is sine inverse. So if sine X equals 0.8973 then X is going to be equal to the inverse sine of 0.8973. In this case, we put our result into our inverse to figure out what value we started with. So let's go ahead and put this expression into our calculator. One thing to note is to remember that these values are in radiance. So in your calculator, you're going to ensure that you see the R ad um the R ad sign probably at the in the top screen of your calculator. And that's for some calculators, for others, it's different, but just ensure that it's in radiance and not degrees. Now, when you put this expression into your calculator, you should find that X equals 1.113614363 approximately. But we're not done yet because remember we want to round our answer to four decimal places. So now we're going to round this value to four decimal places, which means we go to the fourth digit six, look at the digit beside it one. And since it's less than five, we're not going to round up. So to four decimal places, X would be equal to 1.1136. When we look back on our answer choices that would have been answer choice B thanks a lot for watching everyone. I hope this video helped

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.4924

Key Concepts

Sine Function

Inverse Sine Function

Interval [0, π/2]

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