Limits Involving Trigonometric Functions (identities)

In summary, the basic trigonometric identities include sine, cosine, tangent, cotangent, secant, and cosecant, which relate the sides and angles of a right triangle. These identities can be used to solve equations by simplifying them and can also be used to prove other identities by manipulating the equations. The Pythagorean identity, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, is an important trigonometric identity. To avoid mistakes when working with trigonometric identities, it is important to properly simplify expressions, use parentheses when necessary, and consider restrictions on certain trigonometric functions.
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biochem850
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Does anyone know of websites where I can find many problems on the topic in the title line (my textbook has far too few)?

Thanks!
 
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FAQ: Limits Involving Trigonometric Functions (identities)

1. What are the basic trigonometric identities?

The basic trigonometric identities are sine, cosine, tangent, cotangent, secant, and cosecant. These functions relate the sides and angles of a right triangle and can also be expressed as ratios of the sides.

2. How can trigonometric identities be used to solve equations?

Trigonometric identities can be used to simplify equations and expressions involving trigonometric functions. By substituting in the identities, the equations can be reduced to simpler forms that are easier to solve.

3. What is the Pythagorean identity?

The Pythagorean identity, also known as the Pythagorean theorem, states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In terms of trigonometric functions, this can be expressed as sin^2(x) + cos^2(x) = 1.

4. How can trigonometric identities be used to prove other identities?

Trigonometric identities can be used to prove other identities by substituting in known identities and manipulating the equations to show that they are equal. This is often done using algebraic techniques and the properties of trigonometric functions.

5. What are some common mistakes to avoid when working with trigonometric identities?

Some common mistakes to avoid when working with trigonometric identities include: not properly simplifying expressions, not using parentheses when necessary, and forgetting to consider the restrictions on certain trigonometric functions (such as division by zero or undefined values).

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