Trigonometry Test Review

Flashcards created to help review key concepts and formulas related to trigonometry in preparation for an upcoming exam.

What is the period of the function f(x) = 5 cos(6x)+10?

The period P is 2π/6, which simplifies to π/3.

What is the amplitude of the function f(x) = cos[2(x-4)]+6?

The amplitude is 1.

What happens to the function f(x) = -11 sin 3(x-4)+7?

The function has been reflected due to the negative sign before the amplitude.

How do you verify the identity cosx + sinxtanx = secx?

Start by substituting tanx as sinx/cosx and simplifying.

What is the equation for a sine function with no horizontal displacement, rising 4 units above its midline at y = -1?

Y = 4 sin(6x) - 1.

What is the range of the function f(x) = 3.5 sin x?

The range is [-3.5, 3.5].

What is the simplified form of the expression (1 + cos x)(1 - cos x)?

The simplified form is sin² x.

What is the equation for a cosine function that is shifted right by 2π, with a range of 10?

Y = -5 cos(½(x - 2π)).

What is the definition of the amplitude in trigonometric functions?

The amplitude is the maximum distance from the midline to the peak of the wave.

What is the frequency of the function f(x) = sin(3x)?

The frequency is 3/2π.

What is the result of the identity tan²x + 1 = sec²x?

This identity is true as a fundamental Pythagorean identity.

What is the primary function representing the sin (x) oscillation?

The sine function represents vertical oscillation, ranging between -1 and 1.

When is the function cos x + sin x = 0?

The solutions occur at x = 3π/4 + kπ, where k is any integer.

What does the frequency of a periodic function represent?

The frequency indicates how many cycles occur in a unit interval.

What identity can be used to express sec²x?

sec²x can be expressed using the Pythagorean identity sec²x = 1 + tan²x.

What happens to the sine function when it is reflected?

It changes the direction of the oscillation, flipping it vertically.

What is the equation of a sine function that rises 4 units above its midline?

Y = 4 sin(kx) + m, where m represents the midline position.