# Trig - 2nd Degree Equations

• ku07
In summary, to solve the given equation algebraically, one could replace sin(x) with a variable y and solve the resulting quadratic equation for y. Then, the solutions for y could be plugged back into sin(x) to obtain two goniometric equations that can be easily solved. Alternatively, one could treat the equation as a quadratic function and use the quadratic formula or factoring to find the solutions.
ku07
How do you algebraicly find the solution to this equation

6sin(to power of 2)x-6sinx+1=0

where 0<(or equal to) x <(or equal to) 2pi

Let Sinx = u and then use the binomial theorem.

ku07 said:
How do you algebraicly find the solution to this equation

6sin(to power of 2)x-6sinx+1=0

where 0<(or equal to) x <(or equal to) 2pi
If you replace sin(x) by a variable y your equation will be :

$$6y^2 -6y + 1 = 0$$

Solve this equation for y. You will get maximum two solutions for y. each solution is equal to sin(x), so you will get two goniometric equations that will be easy to solve.

marlon

Im in trig as well and I am confused with some of yalls answers. Couldn't he treat this as a quadratic function. If it were me I would see if I could factor it then set each to 0 and solve; if it doesn't factor I would plug it in the quadratic formula and solve. I am in this same chapter of trig so please let me konw what I am overlooking.

seanistic said:
Im in trig as well and I am confused with some of yalls answers. Couldn't he treat this as a quadratic function. If it were me I would see if I could factor it then set each to 0 and solve; if it doesn't factor I would plug it in the quadratic formula and solve. I am in this same chapter of trig so please let me konw what I am overlooking.

yes you can treat it as a quadratic function, that's what marlon did in his post, although you could just leave sin (x) instead of replacing it with y, I believe that just plugging sin(x) = quadratic formula would work just as well, you would then have to do inverse sin on both sides to solve for x

## 1. What is the general form of a 2nd degree equation?

The general form of a 2nd degree equation, also known as a quadratic equation, is ax2 + bx + c = 0, where a, b, and c are constants and x is the variable.

## 2. How many solutions can a 2nd degree equation have?

A 2nd degree equation can have a maximum of two solutions. These solutions can be real or complex numbers.

## 3. How do I solve a 2nd degree equation using the quadratic formula?

To solve a 2nd degree equation using the quadratic formula, first identify the values of a, b, and c in the equation ax2 + bx + c = 0. Then, substitute these values into the formula x = (-b ± √(b2 - 4ac)) / 2a to find the solutions for x.

## 4. Can a 2nd degree equation have no solutions?

Yes, a 2nd degree equation can have no solutions if the discriminant, b2 - 4ac, is negative. In this case, the solutions will be complex numbers.

## 5. How are 2nd degree equations used in real life?

2nd degree equations are used in various fields such as physics, engineering, and economics. They can be used to model and solve real-life problems such as calculating projectile motion, predicting the trajectory of a moving object, and analyzing financial data.

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