Math

QuestionFind the exact value of cos(2π)\cos (-2 \pi) without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the exact value of cos(π)\cos (- \pi). We know that the cosine function, cos(x)\cos(x), is periodic with a period of π\pi. This means that cos(x+π)=cos(x)\cos(x +\pi) = \cos(x) for any real number xx.

STEP 2

Using the periodic property of the cosine function, we can add 2π2\pi to the argument of the cosine function without changing its value.
cos(2π)=cos(2π+2π)\cos(-2\pi) = \cos(-2\pi +2\pi)

STEP 3

implify the argument inside the cosine function.
cos(2π)=cos(0)\cos(-2\pi) = \cos(0)

STEP 4

Recall the value of cos(0)\cos(0) from the unit circle or from memory. The cosine of0 is1.
cos(0)=1\cos(0) =1

STEP 5

Substitute the value of cos(0)\cos(0) back into our equation.
cos(2π)=1\cos(-2\pi) =1The exact value of cos(2π)\cos(-2\pi) is1.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord