anonymous
  • anonymous
Solve: cos² Ɵ + cos Ɵ = 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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cwrw238
  • cwrw238
use the quadratic formula to find values of cos theta
anonymous
  • anonymous
I don't get it, both of the answers :(
.Sam.
  • .Sam.
cos^(2)x+cosx=1 To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side. cos^(2)x+cosx-1=0 Use the quadratic formula to find the solutions. In this case, the values are a=1, b=1, and c=-1. cosx=(-b+-sqrt(b^(2)-4ac))/(2a) where acos^(2)x+bcosx+c=0 Use the standard form of the equation to find a, b, and c for this quadratic. a=1, b=1, and c=-1 Substitute in the values of a=1, b=1, and c=-1. cosx=(-1+-sqrt((1)^(2)-4(1)(-1)))/(2(1)) Simplify the section inside the radical. cosx=(-1+-sqrt(5))/(2(1)) Simplify the denominator of the quadratic formula. cosx=(-1+-sqrt(5))/(2) First, solve the + portion of \. cosx=(-1+sqrt(5))/(2) ----------------------------------------- Next, solve the - portion of \. cosx=(-1-sqrt(5))/(2) ----------------------------------------- The final answer is the combination of both solutions. cosx=(-1+~(5))/(2),(-1-~(5))/(2) ============================= Set up each of the solutions to solve for x. cosx=(-1+sqrt(5))/(2) ,cosx=(-1-sqrt(5))/(2) ---------------------------------------- Set up the equation to solve for x. cosx=(-1+sqrt(5))/(2) Solve the equation for x. \[x=0.9046\pm 2\pi n,5.3786\pm 2\pi n\] --------------------------------------- Set up the equation to solve for x. cosx=(-1-sqrt(5))/(2) Solve the equation for x. Undefined for cosx=(-1-sqrt(5))/(2) but not cosx=(-1+sqrt(5))/(2) -------------------------------------- Only solution is \[x=0.9046\pm 2\pi n,5.3786\pm 2\pi n\]

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