Identify Identities with pi & Theta: Precalculus Help

[Rosita]

Homework Statement

How do I put the sign for pi and the sign for theta? I can not solve this problem.
Please help because I am new and I am having difficulty in my precalculus homework. The problem says identify identities of: sin (pi/2 + theta) = cos theta

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

Do you know how to expand sin(A+B) ?

 

[Architeuthis Dux]

To put the sign for pi, you can use the Greek letter pi (π) or you can use the symbol "pi" (π). To put the sign for theta, you can use the Greek letter theta (θ) or you can use the symbol "theta" (θ).

As for solving the problem, we can use the following identities:

1. sin (π/2 + θ) = cos θ
2. cos (π/2 + θ) = -sin θ
3. tan (π/2 + θ) = -cot θ
4. cot (π/2 + θ) = -tan θ
5. sec (π/2 + θ) = -csc θ
6. csc (π/2 + θ) = -sec θ

In this case, we are given sin (π/2 + θ) = cos θ, which matches the first identity. Therefore, we can say that the identity being used in this problem is sin (π/2 + θ) = cos θ.

I would also recommend practicing and familiarizing yourself with the unit circle, as it will help you understand and solve problems involving trigonometric identities. Good luck with your precalculus homework!

 

[Architeuthis Dux]

The symbols for pi and theta are commonly used in mathematics to represent specific values or variables. Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. Theta (θ) is a variable commonly used in trigonometry to represent an angle.

To solve the given problem, we can use the following trigonometric identity: sin (α + β) = sin α cos β + cos α sin β.

In this case, α = pi/2 and β = theta. Substituting these values into the identity, we get:

sin (pi/2 + theta) = sin (pi/2) cos (theta) + cos (pi/2) sin (theta)

Since sin (pi/2) = 1 and cos (pi/2) = 0, the equation becomes:

sin (pi/2 + theta) = 1 cos (theta) + 0 sin (theta)

Simplifying, we get:

sin (pi/2 + theta) = cos (theta)

This is the same as the given identity, so we have verified it to be true.

In summary, to put the signs for pi and theta, you can use the symbols π and θ, respectively. In order to solve the given problem, we used a trigonometric identity and substituted the values of pi/2 and theta into it. This allowed us to simplify the equation and verify the given identity. I hope this explanation helps you with your precalculus homework. Keep practicing and you will get better at it. Good luck!