QZZ Trig Review

Front

What is the amplitude of a sine function?

Back

The amplitude of a sine function is the maximum value it reaches from its midline. It is represented by the coefficient in front of the sine function, e.g., in y = A sin(Bx), A is the amplitude.

Front

What is the period of a sine or cosine function?

Back

The period of a sine or cosine function is the distance along the x-axis for one complete cycle of the wave. It is calculated as 2π divided by the coefficient of x in the function, e.g., for y = A sin(Bx), the period is 2π/B.

Front

Write the equation for a sine function with an amplitude of 6 and a period of π/4.

Back

y = 6sin(8x) (since the period is π/4, B = 8).

Front

Evaluate sin(225°).

Back

sin(225°) = -√2/2.

Front

What is the period for y = 4cos(1/2x + π) - 2?

Back

The period is 4π (since B = 1/2, the period is 2π/(1/2) = 4π).

Front

What is the value of Arccos(sin(5π/4))?

Back

Arccos(sin(5π/4)) = 3π/4.

Front

What is the general solution of the equation sin(x) = 0?

Back

The general solution is x = 2πn, where n is any integer.

Front

Define the sine function in terms of a right triangle.

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

Define the cosine function in terms of a right triangle.

Back

In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the relationship between sine and cosine functions?

Back

The sine and cosine functions are related by the identity sin(x) = cos(90° - x) or sin(x) = cos(π/2 - x).