Use a calculator to determine whether each statement is true or f...

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.

cos(30° + 20°) = cos 30° + cos 20°

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 cosine of open parentheses. 21 degrees plus 55 degrees closed parentheses is equal to the cosine of degrees plus the cosine of 55 degrees. Our answer choices are answer choice. A true and answer choice B false. All right. So we get to use a calculator. You want to make sure that your calculator is set to degrees mode and now we can simplify what's in parentheses on the left hand side of the equal sign, 21 degrees plus 55 degrees is degrees. So you can plug into the calculator, the cosign of 76 and you hit enter and you'll get a big long number, something like 0. might be longer or shorter. And that's on the left hand side of the equal sign. Now, on the right hand side, when you put in the cosine of 21 degrees, that'll be a big long number and the cosine of 55 degrees. That'll be a big long number to keep it the most accurate. You can just plug in cosine 21 and parentheses plus cosine 55. And you'll get the big long number of 1.507156863. And you can see that 0.24 et cetera is not, not equal to 1.50 et cetera. So these two are not equal. This statement is false. We look at our answer choices and that matches with answer choice. B 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. cos(30° + 20°) = cos 30° + cos 20°

Key Concepts

Cosine Addition Formula

Rounding Errors in Calculations

Trigonometric Identities

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