Write cos(3pi/2 + x) as a Function of x Alone

TL;DR

Understand the cosine function identity to simplify expressions involving cosine and sine.

Transcript

hi in this problem we have to write this as a function of x alone so we have the cosine of 3 pi over 2 plus x so to do this we're going to use an identity the sum identity for the cosine function i'm going to go ahead and write that one down so all the cosine of and instead of x i'm going to use a different letter i'm going to use a and b the cosin... Read More

Key Insights

• 👨‍💼 The cosine function sum identity involves cosine a times cosine b minus sine a times sine b.
• 👨‍💼 Utilize the unit circle to determine cosine and sine values for given angles.
• 🤘 Switch signs for cosine and sine terms according to the cosine function sum identity.
• 😑 Applying the cosine function identity simplifies expressions into functions of x alone.
• 😃 Correctly identifying a and b in the expression is crucial for using the cosine function identity.
• ❣️ The unit circle's x and y coordinates represent cosine and sine values, respectively.
• 👨‍💼 Precise calculation of cosine and sine values is necessary for simplification.

Questions & Answers

Q: How is the cosine function sum identity used in simplifying expressions?

The cosine function sum identity involves cosine a times cosine b minus sine a times sine b, allowing us to simplify expressions by switching signs based on the values of a and b.

Q: What role does the unit circle play in determining cosine and sine values?

The unit circle defines the x and y coordinates of points on the circle as cosine theta and sine theta, respectively, aiding in finding the cosine and sine values for simplification purposes.

Q: How is the expression transformed into a function of x alone using the cosine function identity?

By utilizing the values of a and b in the given expression and applying the cosine function sum identity, the expression is simplified to only involve the function of x without any other variables.

Q: Why is switching signs crucial when using the cosine function sum identity?

Switching signs in the cosine and sine terms according to the cosine function sum identity is essential to accurately simplify expressions and ensure the correct mathematical outcome.

Summary & Key Takeaways

• To write the expression as a function of x alone, use the cosine function sum identity.

• Identify the values of a and b in the given expression and apply the cosine function identity.

• Utilize the unit circle to determine the cosine and sine values required for simplification.