Solve the trig equations 2sin^2(x) + sin(x) - 1 =0

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So, in summary, to find all values of x in the interval 0<=x<=2pi where 2sin^2(x)+sin(x)-1=0, you can use the quadratic formula for trig equations after recognizing that it is a quadratic equation. You can also check your answers by substituting them back into the original equation.
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Trail_Builder
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Homework Statement



Find all values of x in the interval 0<=x<=2pi for which 2sin^2(x)+sin(x)-1=0.

Homework Equations





The Attempt at a Solution



I have no idea.

I spent awhile trying to figure it out on my graphics calculator but couldn't figure it out.

I have only been told how to solve trig equations where there is 1 trig function, lol.

any help would be great thanks.
 
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  • #2
This equation is quadratic, the variable is sin(x). Can you solve now?
 
  • #3
ax^2+bx+c=0

quadratic formula ...

for trig

x=trig identity
 
  • #4
o rite i see.

I think I have the right answers lol

cheeers
 
  • #5
Trail_Builder said:
o rite i see.

I think I have the right answers lol

cheeers
You can always check it by plugging it back into your original equation.
 

What is a trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions, such as sine, cosine, and tangent, and an unknown variable. The goal is to solve for the unknown variable.

How do you solve a trigonometric equation?

To solve a trigonometric equation, you can use algebraic techniques and trigonometric identities. You can also use a calculator or a graphing tool to find approximate solutions.

What are the steps to solve the equation 2sin^2(x) + sin(x) - 1 = 0?

The steps to solve this equation are:

  1. Use the quadratic formula to solve for sin(x).
  2. Use inverse trigonometric functions to find the value of x.
  3. Check your solutions by plugging them back into the original equation.

What are the possible solutions to the equation 2sin^2(x) + sin(x) - 1 = 0?

The possible solutions are x = 0.5π, x = -0.5π, and x = 2π.

What are some real-life applications of trigonometric equations?

Trigonometric equations are used in various fields such as architecture, engineering, physics, and astronomy. They can be used to calculate distances, angles, and heights in real-life scenarios. For example, they can be used to determine the height of a building or the angle of elevation for a satellite dish.

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