Use a calculator to determine whether each statement is true o...

Question

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. tan² 72°25' + 1 = sec² 72°25'

Accepted Answer

Welcome back. I am so glad you're here. We're asked to identify if the given statement is true or false using a calculator. Our given statement is the tangent squared of 42 degrees 13 minutes plus one equals the C can't squared of 42 degrees. 13 minutes. Our answer choices are answer choice. A true and answer choice B false. All right. One very important thing to make sure before you begin, you wanna make sure you're in degree mode on the calculator. And then once you've done that, what you're typing in is you'll hit that tangent function button and then a parentheses will open up for the 42 degrees you put in 42 then you put point and for the 13 minutes, you'll put 13 after the decimal point, close the parentheses and then hit the squared button and then hit plus one and you will get, after you hit, enter 1.818158008. And now for the other side of the equal sign for CCA squared of 42 degrees 13 minutes, we don't have ac camp button on our calculator, but we do know that the C can of X is equal to one divided by the cosine of X. So you can plug this into your calculator by having one divided by. Or you can set that up as a fraction. If you have a fraction button, then you'll have parentheses around the denominator you want the cosine of, and again, it will be 42.13 for the 42 degrees, 13 minutes close parentheses and then close parenthesis, parentheses again and square that and you hit enter and you'll get 1.818158008. And we can see that those are equivalent. And so this is a true statement. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. tan² 72°25' + 1 = sec² 72°25'

Key Concepts

Pythagorean Identity for Tangent and Secant

Angle Conversion and Notation

Rounding Errors in Calculator Computations

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