Question
Given the equation 2cos^2x+sinx-1=0
1. Explain why this equation cannot be factored.
2. Use a trigonometric identity to change the equation into one that can be factored.
1. Explain why this equation cannot be factored.
2. Use a trigonometric identity to change the equation into one that can be factored.
Answers
Steve
can't be factored because different functions are involved.
As if you had y^2+x-1 = 0
But, using a well-known identity connecting sin and cos,
2cos^2 + sin - 1 = 0
2 - 2sin^2 + sin - 1 = 0
2sin^2 - sin - 1 = 0
(2sinx+1)(sinx-1) = 0
As if you had y^2+x-1 = 0
But, using a well-known identity connecting sin and cos,
2cos^2 + sin - 1 = 0
2 - 2sin^2 + sin - 1 = 0
2sin^2 - sin - 1 = 0
(2sinx+1)(sinx-1) = 0