In Exercises 9–16, use the given triangles to evaluate each expre...

Question

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

sin 𝜋/4 - cos 𝜋/4

Accepted Answer

Hello, everyone. We are asked to use the given triangle and find the value of the following expression. Rationalizing the denominator of the final answer. If required, our triangle is a right triangle. ABC with 45 degree angles at both angle A and angle C both legs A B and BC have a measure of one in the hypotenuse AC has a measure of radical two. We are asked to find the value of cosine pi divided by four minus sine pi divided by four. We have four answer choices first. Before I do anything else, I realize that what I'm asked to find pi divided by four is currently ingredients. I want this to be in degrees. I also recall that the easiest way to convert that is to substitute 80 degrees in for pie. So 180 degrees divided by four would leave us with 45 degrees. So pi divided by four is the same as 45 degrees. So now we are looking to find the cosine of 45 degrees minus the sign of 45 degrees. I'm gonna find the value of cosine 45 degrees first and then I'm gonna substitute it in since both angle A and angle C are 45 degrees, it doesn't matter which one I choose. In this case, cosine is gonna be the adjacent side divided by the. So if I think of angle A as my 45 degrees, the side adjacent to it is one, the hypotenuse is radical too. So I want to rationalize this by multiplying top and bottom by radical two. And when I do so I get radical 2/2, a radical two divided by two. Next, I'm gonna find the sign of 45 degrees. And I know that's the opposite side divided by the hot. No, again, if I think of this as angle a opposite, it is the value of one. Our hypotenuse is radical two. So one divided by radical two. I'm gonna rationalize my denominator by multiplying top and bottom by radical two. And I'm left with radical two divided by two. So now I could substitute these values to the expression we were given. So the co sign of 45 is radical two divided by two minus the sign of 45 which is radical two divided by two. When I subtract those things, I get zero. So the cosine of pi divided by four minus the sign of pi divided by four is zero. And that is answer choice D zero have a nice day.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.
sin 𝜋/4 - cos 𝜋/4