banfill_89 said:Homework Statement
cos^2 x-cos x- 1= 0
Homework Equations
several trig identities involving cos
The Attempt at a Solution
i tried applying identites everywhere, no luck. I've tried using it as a trinomial...no luck...and I've tried adding one to both sides and still no luck...please help lol
The interval between 0 and 2pi is known as one "cycle" of the unit circle, meaning that values within this range will repeat themselves. Therefore, solving trig equations within this interval allows us to find all possible solutions for a given equation.
To solve trig equations in this interval, we use the properties of trigonometric functions such as sine, cosine, and tangent, along with algebraic techniques. We manipulate the equation to isolate the variable and then use inverse trigonometric functions to find the solutions within the given interval.
Yes, a trig equation can have multiple solutions within this interval. This is because the trigonometric functions are periodic, meaning that they repeat themselves every 2pi. Therefore, there can be an infinite number of solutions within this range.
Yes, there are a few special cases to keep in mind when solving trig equations in this interval. These include when the equation has a coefficient in front of the trig function, when the equation is in terms of the cotangent function, and when the equation involves inverse trigonometric functions.
Solving trig equations in this interval has practical applications in fields such as physics, engineering, and astronomy. For example, it can be used to calculate the position of an object in circular motion, the height of a building, or the trajectory of a projectile.