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olga2289 [7]
1 year ago
9

Please help, performance task: trigonometric identities

Mathematics
1 answer:
AnnZ [28]1 year ago
4 0

The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

<h3>How to solve the trigonometric equations?</h3>

<u>Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)</u>

The equation can be split as follows:

y = 1 - cos(x)

y = 2 - 2sin²(x)

Next, we plot the graph of the above equations (see graph 1)

Under the domain interval (-π, π), the curves of the equations intersect at:

(-π/3, 0.5) and (π/3, 0.5)

Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

<u>Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)</u>

The equation can be split as follows:

y = 4cos⁴(x) - 5cos²(x) + 1

y = o

Next, we plot the graph of the above equations (see graph 2)

Under the domain interval [0, 2π), the curves of the equations intersect at:

(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Read more about trigonometry equations at:

brainly.com/question/8120556

#SPJ1

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