Solving Trig Equations: Tips, Tricks, and Strategies for All Values of x (0-360)

Thread starter Hootenanny
Start date Mar 7, 2006
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In summary, a trigonometric equation is an equation that involves trigonometric functions and can be solved to find the values of the unknown variable. Common strategies for solving these equations include algebraic manipulation, trigonometric identities, and the unit circle. To solve for all values of x from 0 to 360 degrees, the unit circle and reference angles can be used, along with the periodicity of trigonometric functions. Tips for solving these equations more efficiently include identifying patterns, simplifying expressions, and practicing regularly. An example of solving a trigonometric equation is solving sin(x) = 0.5 for all values of x from 0 to 360 degrees, with solutions of x = 30, 150,

Mar 7, 2006

Hootenanny

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The question is to solve the equation;
[tex]2\cot^{2}x + 7cosec x - 13 = 0 [/tex]
for all values of x between 0 and 360. I know I need to use a trig ident, but I've been using several over the course of an hour and I can't seem to get anywhere. Any hints would be helpful

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Mar 7, 2006

vaishakh

Multiply with sin^2x

Mar 7, 2006

Lyuokdea

try using cot(x)^2 + 1 = csc(x)^2

~Lyuokdea

Mar 7, 2006

Hootenanny

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Thank's got it.

FAQ: Solving Trig Equations: Tips, Tricks, and Strategies for All Values of x (0-360)

What is a trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, and tangent. These equations can be solved to find the values of the unknown variable, typically represented by x.

What are some common strategies for solving trigonometric equations?

Some common strategies for solving trigonometric equations include using algebraic manipulation, applying trigonometric identities, and using the unit circle to find reference angles.

How do I solve trigonometric equations for all values of x from 0 to 360 degrees?

To solve trigonometric equations for all values of x from 0 to 360 degrees, you can use the unit circle and reference angles. You can also use the periodicity of trigonometric functions to determine the solutions that fall outside of the given range.

What are some tips for solving trigonometric equations more efficiently?

Some tips for solving trigonometric equations more efficiently include identifying patterns and using the appropriate trigonometric identities, simplifying expressions, and practicing regularly to become familiar with common trigonometric values.

Can you provide an example of solving a trigonometric equation?

Sure, an example of solving a trigonometric equation is solving the equation sin(x) = 0.5 for all values of x from 0 to 360 degrees. Using the unit circle, we can see that the solutions are x = 30 degrees and x = 150 degrees, as these angles have a sine value of 0.5. We can also use the periodicity of trigonometric functions to find additional solutions, such as x = 210 degrees and x = 330 degrees.