Solving Trig Equations: Tips and Tricks for Finding Solutions

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In summary, a trigonometric solution is a mathematical solution that involves the use of trigonometric functions. To solve a trigonometric equation, you can use algebraic techniques, trigonometric identities, or a calculator. The unit circle, which is a circle with a radius of 1 unit, is used in trigonometry to relate the values of trigonometric functions to the coordinates of points on the circle. Some common trigonometric identities include the Pythagorean identities, double-angle identities, and sum and difference identities. Trigonometric functions are widely used in many real-life applications such as engineering, physics, navigation, and astronomy. They can help calculate distances, angles, and heights, as well as model periodic phenomena
  • #1
jamjar
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Hi,
I'm trying to solve this trig equation. I've tried representing everything in terms of sin or cos but I don't ever seem to get anywhere useful.
Any pointers?

[tex]Sin(\theta ) = \frac{1}{2}\left( {\frac{1}{{Cos(\theta )}} + Cos(\theta )} \right)
[/tex]
 
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  • #2
Well, I just solved that anyway, 1 minute after posting it.
I had some wacky manipulation error before that I spotted.
 
  • #3
How did you solve it? I have been studying this problem and I cannot find a solution.
 

Related to Solving Trig Equations: Tips and Tricks for Finding Solutions

What is the definition of a trigonometric solution?

A trigonometric solution is a mathematical solution to a problem that involves the use of trigonometric functions, such as sine, cosine, and tangent.

How do I solve a trigonometric equation?

To solve a trigonometric equation, you can use algebraic techniques, trigonometric identities, or a calculator. First, isolate the trigonometric function on one side of the equation. Then, use inverse trigonometric functions or trigonometric identities to simplify the equation. Finally, use a calculator to find the numerical solution.

What is the unit circle and how is it related to trigonometry?

The unit circle is a circle with a radius of 1 unit. It is used in trigonometry to relate the values of trigonometric functions to the coordinates of points on the circle. The x-coordinate represents the cosine value and the y-coordinate represents the sine value.

What are the common trigonometric identities?

Some common trigonometric identities include the Pythagorean identities (sin²θ + cos²θ = 1), the double-angle identities (sin 2θ = 2sinθcosθ), and the sum and difference identities (sin (α ± β) = sinαcosβ ± cosαsinβ).

How are trigonometric functions used in real life?

Trigonometric functions are used in many real-life applications, including engineering, physics, navigation, and astronomy. They can be used to calculate distances, angles, and heights, as well as to model periodic phenomena such as sound waves and electromagnetic waves.

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