Solving Trig Functions for Simplifying Equations and Finding Solutions

In summary, trigonometric functions are mathematical functions used to relate angles to the sides of right triangles. The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant, and they are defined by the ratios of the sides of a right triangle. To solve trigonometric functions, one must identify the given information and unknown variable, and then use trigonometric identities, laws, and rules to simplify the function. The most common strategies for solving trigonometric functions include using the unit circle, applying trigonometric identities, using the Pythagorean theorem, and using the trigonometric ratios of special angles. Calculators can also be used to solve trigonometric functions, but it
  • #1
alanp1950
1
0

Homework Statement



I was asked how to go about solving for t

Homework Equations




140=10t + sin(t)

The Attempt at a Solution



I used a graphical solution, is there an easier way
 
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  • #2
Not really. There's no way to solve that algebraically in terms of any special functions I know of.
 
  • #3
?

I would recommend using algebraic methods to solve for t in this equation. While graphical solutions can be helpful, they may not always provide the most accurate or efficient solution. To solve for t in this equation, you can use trigonometric identities and properties to simplify the equation and isolate t. For example, you can use the double angle formula for sine or the Pythagorean identity to simplify the equation and solve for t. Additionally, you can also use the inverse trigonometric functions (such as arcsine) to solve for t. These methods may be more straightforward and precise in finding the solution for t.
 

FAQ: Solving Trig Functions for Simplifying Equations and Finding Solutions

1. What are trigonometric functions?

Trigonometric functions are mathematical functions that relate angles to the sides of right triangles. They are commonly used in solving problems involving triangles and in fields such as physics, engineering, and astronomy.

2. What are the six basic trigonometric functions?

The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. These functions are defined by the ratios of the sides of a right triangle.

3. How do you solve trigonometric functions?

To solve trigonometric functions, you must first identify the given information and the unknown variable. Then, you can use trigonometric identities, laws, and rules to simplify the function and solve for the unknown variable.

4. What are the most common strategies for solving trigonometric functions?

The most common strategies for solving trigonometric functions include using the unit circle, applying trigonometric identities, using the Pythagorean theorem, and using the trigonometric ratios of special angles such as 30°, 45°, and 60°.

5. Can you use a calculator to solve trigonometric functions?

Yes, calculators can be used to solve trigonometric functions. Most scientific and graphing calculators have built-in functions for sine, cosine, tangent, and their inverse functions. However, it is important to understand the concept and steps of solving trigonometric functions before relying solely on a calculator.

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