Textbook Question
Solve each equation for exact solutions over the interval [0, 2π).
―2 sin² x = 3 sin x + 1
5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Linear Trigonometric Equations
Multiple Choice
Find all solutions to the equation.
A
B
C
D
Verified step by step guidance1
Start by understanding the equation \( \cos x = 1 \). The cosine function equals 1 at specific points on the unit circle.
Recall that the cosine function has a period of \( 2\pi \), meaning it repeats every \( 2\pi \) radians.
The cosine of an angle is 1 at \( x = 0 \) and repeats every \( 2\pi \), so the general solution is \( x = 2\pi n \), where \( n \) is an integer.
Consider other angles where cosine might equal 1, but note that \( \cos x = 1 \) only at \( x = 0 \) and its periodic repetitions.
Thus, the complete set of solutions for \( \cos x = 1 \) is \( x = 2\pi n \), where \( n \) is any integer.
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