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.

sec s = 1.0806

Accepted Answer

Welcome back. I am so glad you're here. We're told, considering the interval from zero to pi divided by two inclusive of both, find the approximate value of X express your answer in four decimal places. We're told that the C can of X equals 1.2937. Our answer choices are answer choice. A 0.6873. Answer choice B 0.7255 answer choice C 0.6314 and answer choice D 0.7883. All right. So we're trying to solve for X, which is the angle here. We know what the C of X is equal to. So when we're trying to find that angle, we are going to use the inverse of this trigonometric functions button on our calculators. However, there is no inverse C can't button on the calculator. So what do we do? Well, we know that C can has a reciprocal function and that is cosine, we recall from previous lessons that the cosine of X of any angle here X is equal to one divided by the C can't of that same angle here. X. So we can use substitution here. We have the C can of X in the denominator and we'll substitute what the C can of X is equal to which is 1.2937. So let's rewrite this. The cosine of X equals one divided by instead of the C can of X 1.2937. And now we can use the inverse cosine button on the calculator. First, make sure that you are in radiance mode, not degrees. And you're going to punch in the cosine, raise to the negative one. That's the inverse cosine button. It'll give you a parenthesis. And here you want to put in one divided by 1.2937 close parentheses and hit enter, you'll get something like 0.68727. That'll keep going. But we're rounding to four decimal places. The fourth decimal place here is a two. It looks to the seven and it rounds up. So X is equal to 0.6873. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

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

sec s = 1.0806

Key Concepts

Secant Function

Inverse Trigonometric Functions

Interval Restrictions

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