Use a calculator to evaluate each expression.

cos 75°29' cos 14°...

Question

Use a calculator to evaluate each expression.

cos 75°29' cos 14°31' - sin 75°29' sin 14°31'

Accepted Answer

Hello, everyone. We are asked to evaluate the following expression by using a calculator. We are given the cosine of 43 degrees 27 minutes multiplied by the cosine of 46 degrees. 33 minutes minus the sign of 43 degrees. 27 minutes multiplied by the sign of 46 degrees. 33 minutes. Our answer choices are a one B, one half C negative one D zero. So the first thing I wanna do, my calculator won't let me enter this in degrees in minutes. There's a couple ways I could get around that. The way that I think might be easiest is if I take degrees 27 minutes, I could treat it as 43 degrees, 27 divided by 60 degrees, add them together. And I'll find the decimal for 27 divided by 60. And this will give me 43.45 degrees. This will enter into my calculator a lot easier. I'm gonna do the same thing with 46 degrees, 33 minutes. So again, the 46 degrees part will stay and we're gonna add 33 divided by 60 as they're 60 minutes in one degree, we will find the decimal equivalent to this and we can rerate this as 46.55 degrees. So now I'm gonna rewrite my expression with my decimal degrees. So I will have the cosine of 43.45 degrees multiplied by the cosine of 46. degrees minus the sign of 43.45 degrees multiplied by the sign of 46.55 degrees. Make sure your calculator is in degree mode. But after that, you should be able to type this entire expression in at once. And when we do, I find that this entire expression equals zero. And that's answer choice. D have a nice day.

Use a calculator to evaluate each expression. cos 75°29' cos 14°31' - sin 75°29' sin 14°31'

Key Concepts

Cosine and Sine Functions

Angle Addition Formula

Degrees and Minutes

Watch next