The solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.
How to solve trigonometric equations
Trigonometric functions are periodic functions, cosine function has a standard period of 2π radians. There are two approaches to solve the expression given, an analytical one and a graphical one. Now we proceed to show each approach:
Analytical method
Now we proceed to apply algebraic handling and inverse trigonometric functions to solve the expression for t:
7 · cos 2t = 3
cos 2t = 3/7
2 · t = cos⁻¹ (3/7)
There are two solutions:
2 · t₁ ≈ 0.359π + 2π · i ∨ 2 · t₂ ≈ 1.641π + 2π · i
t₁ ≈ 0.180π + π · i ∨ t₂ ≈ 0.821π + π · i
t₁₁ ≈ 0.180π ∨ t₁₂ ≈ 1.180π ∨ t₂₁ ≈ 0.821π ∨ t₂₂ ≈ 1.821π
The solutions of the trigonometric equations in [0, 2π] are approximately 0.18π, 0.82π, 1.18π and 1.82π.
Graphical approach
First, we add the definition of the following two functions (f(x) = 7 · cos 2t and g(x) = 3) and plot in the calculator through a graphing tool. The solutions of this trigonometric function are the points of intersection of the two functions.
According to the image attached below, the solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.
To learn more on trigonometric equations: https://brainly.com/question/23948746
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