How do I simply this (there should be a trig. identity involved

In summary, to simplify a trigonometric identity involving sine and cosine, you can use fundamental identities such as the Pythagorean identity or double angle identities, as well as basic algebraic techniques like factoring and combining like terms. It is not recommended to rely solely on a calculator for simplification. Choosing the right identity to use depends on the given expression and goal of simplification. You can manipulate both sides of an identity as long as the same operation is performed on both sides. Some tips for simplifying complicated identities include breaking the expression into smaller parts, using double angle identities, and substituting trigonometric functions with their corresponding reciprocal functions. Practicing and becoming familiar with fundamental identities can also be helpful.
  • #1
Linus Pauling
190
0
1. This was actually a center of mass problem, so I got the equation below:



2.[T_2*sin(theta2)] / [T_1*sin(theta1) + T_2*sin(theta2)]



3. This is part of a solution I obtained for a physics problem. I know there is some trick with a trig indentity that I can use to simplify this. What is the identity?
 
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  • #2
Here's a visual aid:

MTS_st_24.jpg
 
  • #3


The identity that can be used to simplify this equation is the sine addition formula, which states that sin(a+b) = sin(a)*cos(b) + sin(b)*cos(a). This can be applied to the numerator and denominator of the equation to simplify it to [T_2*sin(theta2)] / [T_1*sin(theta1)*cos(theta2) + T_2*sin(theta2)*cos(theta1)]. This can then be further simplified using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, to eliminate the cosine terms and ultimately obtain a simpler expression.
 

FAQ: How do I simply this (there should be a trig. identity involved

How do I simplify a trigonometric identity involving sine and cosine?

To simplify a trigonometric identity involving sine and cosine, you can use the fundamental identities such as the Pythagorean identity or the double angle identities. Remember to also use basic algebraic techniques such as factoring and combining like terms.

Can I use a calculator to simplify a trigonometric identity?

While a calculator can provide you with numerical values for trigonometric functions, it is not recommended to solely rely on a calculator to simplify a trigonometric identity. It is important to understand the fundamental identities and use them to simplify the expression by hand.

How do I know which trigonometric identity to use when simplifying an expression?

Choosing the right trigonometric identity to use when simplifying an expression depends on the given expression and the goal of simplification. It is important to be familiar with the various identities and their applications in order to make the best choice.

Can I manipulate both sides of a trigonometric identity when simplifying it?

Yes, you can manipulate both sides of a trigonometric identity when simplifying it, as long as the same operation is performed on both sides. For example, you can add the same term to both sides or multiply both sides by the same value.

What are some tips for simplifying complicated trigonometric identities?

Some tips for simplifying complicated trigonometric identities include: breaking the expression into smaller parts, using the double angle identities, and substituting trigonometric functions with their corresponding reciprocal functions (e.g. secant for cosine). It is also helpful to practice and become familiar with the fundamental identities.

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