lylos said:The Attempt at a Solution
Tan[60 degrees]=Sin[theta]/(1/3+Cos[theta])
(1/3+Cos[theta])Tan[60 degrees]=Sin[theta]
1/3 Tan[60 degrees]=Sin[theta]-Tan[60 degrees]*Sin[theta]
A trigonometric equation is an equation that involves one or more trigonometric functions, such as sin, cos, tan, sec, csc, or cot. These equations are used to solve for unknown angles or sides in a triangle, using the relationships between the sides and angles in a triangle.
To solve a trigonometric equation, you need to isolate the variable (usually an angle) on one side of the equation. Then, use the inverse trigonometric functions (such as arcsin, arccos, or arctan) to find the value of the angle. Lastly, check your solution by plugging it back into the original equation.
The most commonly used trigonometric identities are the Pythagorean identities (sin^2x + cos^2x = 1 and tan^2x + 1 = sec^2x), the double angle identities (sin2x = 2sinx cosx and cos2x = cos^2x - sin^2x), and the half angle identities (sin(x/2) = ±√[(1-cosx)/2] and cos(x/2) = ±√[(1+cosx)/2]).
Some tips for solving tricky trigonometric equations include: using the unit circle to determine the values of trigonometric functions at common angles, using trigonometric identities to rewrite the equation in a simpler form, and checking for extraneous solutions (solutions that do not satisfy the original equation).
You can check your solution to a trigonometric equation by plugging it back into the original equation and simplifying both sides. If the resulting equation is true, then your solution is correct. You can also graph both sides of the equation and see if they intersect at the value you found for the variable.