Understanding Trigonometric Functions

This video tutorial explains how to graph trigonometric functions without plotting each point individually. It covers the concepts of amplitude and period, demonstrating how to calculate these using formulas. The tutorial provides a step-by-step guide to graphing a sine function, highlighting the differences between sine and cosine functions. It also discusses how to identify these functions from their graphs and introduces the concept of shifting, which will be explored in future modules.

What is the main goal of the presentation?

• To solve trigonometric equations.

• To memorize trigonometric identities.

• To understand the analytic definition of trig functions.

• To learn how to graph trig functions point by point.

In the function f(x) = 2 sin(1/2 x), what does the coefficient 2 affect?

• The frequency of the function.

• The period of the function.

• The amplitude of the function.

• The phase shift of the function.

How is the period of the function f(x) = 2 sin(1/2 x) calculated?

• By multiplying the coefficient of x by 2π.

• By dividing 2π by the coefficient of x.

• By adding 2π to the coefficient of x.

• By subtracting the coefficient of x from 2π.

What is the period of the function f(x) = 2 sin(1/2 x)?

• 1/2π

• 4π

• π

• 2π

What is the amplitude of the function f(x) = 2 sin(1/2 x)?

• 1

• 2

• 1/2

• 4

How can you determine if a function is sine or cosine based on its graph?

• By checking the value at x = 0.

• By checking the period.

• By checking the frequency.

• By checking the amplitude.

What is the value of f(0) for the function f(x) = 2 sin(1/2 x)?

• 0

• 1

• 2

• -2

What is the value of f(0) for the function f(x) = 2 cos(1/2 x)?

• -2

• 2

• 1

• 0

How does the graph of cosine differ from sine without shifting?

• Cosine starts at 0, sine starts at -1.

• Cosine starts at 0, sine starts at 1.

• Cosine starts at -1, sine starts at 0.

• Cosine starts at 1, sine starts at 0.

What happens to the graph of cosine when it is shifted by π/2?

• It becomes a sine graph.

• It becomes a tangent graph.

• It becomes a cotangent graph.

• It becomes a secant graph.