Solve 2sin^2x+cosx-1=0 (fast in 3.2 minutes, no details skipped)

🧮 Solve 2sin^2x+cosx-1=0 in 3.2 minutes (Fast & Easy) 🚀 | Learn how to solve trigonometric equations

In this video, we will learn how to solve the trigonometric equation 2sin^2x+cosx-1=0 in just 3.2 minutes! We won't skip any details, and we'll use the Pythagorean identity and substitution to find the solution quickly.

To solve this equation, we first use the Pythagorean identity to rewrite sine squared x as 1-cosine squared x. We then substitute this into the equation and simplify it by distributing and grouping like terms. We use the substitution u=cosx to factor the resulting quadratic equation, and we find the values of u that satisfy the equation. We then use the unit circle to find the corresponding values of x that satisfy the equation.

The solutions are x=2π/3 and 4π/3 when cosine x=-1/2, and x=0 and 2π when cosine x=1.

If you're struggling to solve trigonometric equations, this video is for you! Don't forget to leave a like if you find this helpful. 🔥

🔑 Keywords trigonometric equation, solve, Pythagorean identity, substitution, quadratic equation, unit circle, cosine, fast, easy, tutorial.

🤔 Common questions
1️⃣ How do you solve trigonometric equations?
To solve trigonometric equations, you use trigonometric identities and properties to rewrite the equation in terms of a single trigonometric function. You then use algebraic techniques to solve the resulting equation.

2️⃣ What is the Pythagorean identity?
The Pythagorean identity is a trigonometric identity that relates the values of sine and cosine for any angle in a right triangle. It states that sin^2x+cos^2x=1.

3️⃣ How do you factor quadratic equations?
To factor quadratic equations, you look for two numbers that multiply to give you the constant term and add to give you the coefficient of the linear term. You then rewrite the quadratic equation as the product of two binomials.

4️⃣ What is the unit circle?
The unit circle is a circle with a radius of 1 centered at the origin of a Cartesian coordinate system. It is used to define the values of sine and cosine for any angle in radians or degrees.

5️⃣ What is cosine?
Cosine is a trigonometric function that relates the ratio of the adjacent side to the hypotenuse of a right triangle for any angle.

6️⃣ What is a quadratic equation?
A quadratic equation is an equation of the form ax^2+bx+c=0, where a, b, and c are constants and x is the variable.

7️⃣ What is substitution in algebra?
Substitution is a technique in algebra where you replace one variable with an expression that is equivalent to the variable in an equation or expression. This technique can simplify the equation or expression and make it easier to solve.