Question ,trigonometric identities equation and functions ?

In summary, trigonometric identities are true for all values of theta, while equations are only true for certain values of theta. A trigonometric function involves trigonometric ratios of a variable. Numerical methods can be applied to solve equations involving trigonometric functions, such as the example of sin theta = cos (theta + x). Some examples of numerical methods in trigonometry include substituting different values for theta and checking for solutions, such as when sin theta = cos (theta + x).
  • #1
awholenumber
200
10
what is the difference between trigonometric identities , equations and functions ...?

is it possible to apply some numerical method on a trigonometric function ??

i was looking for an example where numerical methods could be applied on a trigonometric function ...

i am not sure what you could achieve with that at this point of time...

also ... is this a trigonometric function ??

f(x) = A sin (kx-wt)

??
 
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  • #2
Identities like sin^theta + cos^2 theta = 1 are true for all values of theta. Equations like sin theta = cos (theta +x) is true for some value or values of theta only. Any function involving trigonometric ratios of variable can be called trigonometric function. Yes I think numerical methods can be applied here. try to apply it to solve teh equation quoted in this post.
 
  • #3
Let'sthink said:
Identities like sin^theta + cos^2 theta = 1 are true for all values of theta. Equations like sin theta = cos (theta +x) is true for some value or values of theta only. Any function involving trigonometric ratios of variable can be called trigonometric function. .

thanks for that ...

i am not familiar with the numerical methods associated with trigonometry right now ...

could someone tell me few examples of it ??
 
  • #4
just put different values of theta and take some say x = 30 degree. and check when sin theta = cos(theta+30).
 
  • #5
thanks for the answers ..

i will surely try when i get some free time ...
 

1. What are trigonometric identities?

Trigonometric identities are equations that involve trigonometric functions (such as sine, cosine, and tangent) and are true for all values of the variables within a certain range. They are used to simplify and solve trigonometric equations and can also be used to prove other mathematical statements.

2. What is the difference between an equation and an identity?

An equation is a statement that shows the equality between two expressions, while an identity is a specific type of equation that is true for all values of the variables. In other words, an identity is a special case of an equation where both sides are always equal, whereas an equation may only be true for certain values of the variables.

3. How do you verify a trigonometric identity?

To verify a trigonometric identity, you must manipulate one side of the equation using algebraic and trigonometric properties until it is equivalent to the other side of the equation. This process may involve factoring, expanding, using trigonometric identities, and substituting values for trigonometric functions.

4. What are some common trigonometric identities?

Some common trigonometric identities include the Pythagorean identities (such as sin²θ + cos²θ = 1), the double angle identities (such as sin(2θ) = 2sinθcosθ), and the sum and difference identities (such as sin(α ± β) = sinαcosβ ± cosαsinβ). There are many more identities that can be derived from these basic ones.

5. How are trigonometric identities used in real life?

Trigonometric identities are used in many fields, including engineering, physics, and astronomy, to solve problems involving angles and distances. They are also used in navigation and surveying to calculate distances and bearings. In addition, they are used in computer graphics and animation to create realistic images and movements.

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