Unit 8 DO NOW

Front

What is the period of a sine or cosine graph?

Back

The period is the distance (in the x-direction) it takes for the graph to complete one full cycle. For the function y = A sin(Bx) or y = A cos(Bx), the period is given by the formula: Period = \frac{2\pi}{|B|}.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: Radians = Degrees × \frac{\pi}{180}.

Front

What is the midline of a trigonometric graph?

Back

The midline is a horizontal line that runs through the middle of the graph, representing the average value of the function. For the function y = A sin(Bx) + D, the midline is y = D.

Front

What is the formula for the length of an arc in a circle?

Back

The length of an arc (s) can be calculated using the formula: s = rθ, where r is the radius and θ is the angle in radians.

Front

What is the sine function?

Back

The sine function relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse. It is defined as: sin(θ) = \frac{opposite}{hypotenuse}.

Front

What is the cosine function?

Back

The cosine function relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is defined as: cos(θ) = \frac{adjacent}{hypotenuse}.

Front

What is the tangent function?

Back

The tangent function relates the angle of a right triangle to the ratio of the length of the opposite side to the adjacent side. It is defined as: tan(θ) = \frac{opposite}{adjacent}.

Front

What is the relationship between sine and cosine?

Back

The sine and cosine functions are related through the Pythagorean identity: sin²(θ) + cos²(θ) = 1.

Front

How do you find the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph. For the function y = A sin(Bx) or y = A cos(Bx), the amplitude is |A|.

Front

What is the phase shift of a trigonometric function?

Back

The phase shift is the horizontal shift left or right for the graph of a trigonometric function. For the function y = A sin(B(x - C)), the phase shift is C.