SUMMARY
The equation 2cos²x - cos x = 0 can be systematically solved by treating it as a quadratic equation in terms of cos x. By substituting cos x with a variable, such as Z, the equation transforms into 2Z² - Z = 0. Factoring this yields Z(2Z - 1) = 0, leading to the solutions Z = 0 and Z = 1/2. Consequently, the angles x corresponding to these values within the interval [0, 360] are x = 90°, 270° for Z = 0 and x = 60°, 300° for Z = 1/2.
PREREQUISITES
- Understanding of trigonometric functions and their properties
- Knowledge of quadratic equations and factoring techniques
- Familiarity with the unit circle and angle measurement in degrees
- Ability to solve for variable substitutions in equations
NEXT STEPS
- Study the properties of trigonometric identities and their applications
- Learn about solving quadratic equations using the quadratic formula
- Explore the unit circle to understand angle values for trigonometric functions
- Investigate the graphical representation of trigonometric equations
USEFUL FOR
Students, educators, and anyone interested in mastering trigonometric equations and their systematic solutions.