Trigonometry and Programming Basics Quiz

Trigonometric Identity

• The equation ( \sin^2 x + \cos^2 x = 1 ) represents a fundamental Pythagorean identity in trigonometry.
• This identity holds true for all angles ( x ) and is widely used in various mathematical applications.

Programming Syntax

• The code snippet print("Hello World"[[: represents an incomplete slice operation in Python, leading to a syntax error.
• Proper string slicing in Python requires specifying both start and end indices, hence the absence of a complete syntax would cause the program to fail.

Options for Question 1

• None of these: Incorrect; the correct answer is a well-established identity.
• 1: This is the correct simplification of ( \sin^2 x + \cos^2 x ).
• 2 sin(x) cos(x): This expression equals ( \sin(2x) ) but is not related to the given equation.
• ( \tan^2 x ): Incorrect; this does not relate to the Pythagorean identity.

Test your understanding of basic trigonometric identities and simple programming concepts. Evaluate your skills in simplifying trigonometric expressions and identifying errors in code snippets.