Find the general solution of the equation cos(2x) = 0.
Practice Questions
Q1
Find the general solution of the equation cos(2x) = 0.
x = (2n+1)π/4
x = nπ/2
x = (2n+1)π/2
x = nπ
Questions & Step-by-Step Solutions
Find the general solution of the equation cos(2x) = 0.
Correct Answer: x = (2n+1)π/4, where n is any integer.
Step 1: Start with the equation cos(2x) = 0.
Step 2: Recall that cosine equals zero at specific angles. The angles where cos(θ) = 0 are θ = (2n + 1)π/2, where n is any integer.
Step 3: Set 2x equal to the angles where cosine is zero: 2x = (2n + 1)π/2.
Step 4: Solve for x by dividing both sides of the equation by 2: x = (2n + 1)π/4.
Step 5: Write the final answer, which is the general solution: x = (2n + 1)π/4, where n is any integer.
Trigonometric Equations – The question tests the understanding of solving trigonometric equations, specifically using the cosine function and its properties.
General Solutions – It assesses the ability to find the general solution for periodic functions, which involves understanding the periodic nature of trigonometric functions.
