Find all solutions (x) of sec^2(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 determined above using exact values, not decimal approximations using the symmetry of the circle.
Find all solutions (x) of sec^2(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 determined above using exact values, not decimal approximations using the symmetry of the
D.) Sketch a graphical interpretation of the solutions (u) in the interval determined, and the solutions (x) in the interval [0,2pi) and explain the relationship between these.
E.) Express the set of all possible solutions to the equation, in set notation using k € Z to denote integers.
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