Find all solutions x of sec (3x) = 25 within the interval [0, 2pi] using the...
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Find all solutions x of sec² (3x) = 25 within the interval [0, 2pi] using the following process: a) Rewrite the equation using a reciprocal identity. b) Write the interval constraint for x as an inequality statement, and use this to determine what interval you will look in for solutions u =3x c) Solve the equation using the substitution u = 3x for all solutions in the interval you determined above. (These should be exact values) d) Sketch a graphical interpretation of the solutions u in the interval you determined, and the solutions x in the interval [0, 2pi]. Explain the relationship between these. Express the set of all possible solutions to the equation, in set notation using k EZ to denote integers. Find all solutions x of sec² (3x) = 25 within the interval [0, 2pi] using the following process: a) Rewrite the equation using a reciprocal identity. b) Write the interval constraint for x as an inequality statement, and use this to determine what interval you will look in for solutions u =3x c) Solve the equation using the substitution u = 3x for all solutions in the interval you determined above. (These should be exact values) d) Sketch a graphical interpretation of the solutions u in the interval you determined, and the solutions x in the interval [0, 2pi]. Explain the relationship between these. Express the set of all possible solutions to the equation, in set notation using k EZ to denote integers.
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a Reciprocal identity for secant is secx 1cosx So we can rewrite the equation as 1cos3x 25 b We need ... View the full answer
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