In Exercises 25–30, use an identity to find the value of each exp...

Question

In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator.

sin² 𝜋 + cos² 𝜋
      10          10

Accepted Answer

Hello, everybody. I hope you are doing all right. Today, today, we're going to be looking at this question that states without using a calculator determine the value of the following trigonometric expression where our expression is open bracket. Sign of open parentheses, pi divided by 21 closed parentheses, closed bracket squared plus open bracket, cosine of open parentheses, pi divided by 21 closed parentheses, closed bracket squared. Now the answer to providing are a zero B one C negative two and D one half. Now as we tackle this question, the very, very first thing we're going to do is recall a rule that we know about Trigon metric functions. So we can recall that if we have sine squared X plus cosine squared X, that will be equal to one. And this is known as a Python identity. So using that information, let's rewrite what we have. Let's say if X is equal to pi divided by 21 then we can rewrite our equation to have open bracket sign of X, close bracket squared plus open bracket cosine of X, close bracket squared. And that can be rewritten as sine squared, X plus cosine squared. X. And as we said, with our Python identity, this will be equal to one and that matches with answer choice B. So although we started with something that looked a bit complicated by doing a simple recall of a Python identity, we were able to rewrite our equation and solve for the simple answer of one. So I hope that was helpful. And until next time.

In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator. sin² 𝜋 + cos² 𝜋 10 10

Key Concepts

Pythagorean Identity

Values of Trigonometric Functions at Specific Angles

Simplifying Trigonometric Expressions

Watch next