Pre-Calculus Review Flashcards

Flashcards based on Pre-Calculus 4th Nine Weeks Review

What is the formula for the sum of an infinite geometric series?

S = a / (1 - r), where |r| < 1

How can sigma notation be used to express the total earnings with annual raises?

Σ (initial salary * (1 + raise percentage)^n), where n goes from 0 to number of years - 1

What is the formula to find the sum of a geometric series?

S = a1(1 - r^n) / (1 - r)

How do you find the total number of seats in an auditorium where each row adds one seat?

Use the arithmetic series sum formula: S = (n/2)(first row seats + last row seats)

What is a recursive formula for population growth based on a percentage increase?

Pn = Pn-1 * (1 + growth rate)

In an arithmetic sequence, what is the formula for finding the nth term?

an = a1 + (n - 1) * d, where d is the common difference

How to determine angles represented by a terminal side in a diagram?

Add or subtract multiples of 2π (or 360°) to the given angle.

How do you find a reference angle?

Reference angles are the acute angles formed by the terminal side of an angle and the x-axis. Find the difference between the angle and the nearest x-axis (180 or 360)

What is the location of the intersection point of the terminal side on the unit circle related to?

The coordinates correspond to (cos θ, sin θ)

If given tan θ, how do you find other trigonometric values?

Use trigonometric identities and the Pythagorean theorem to find the remaining values.

How do you convert feet to inches?

Multiply the number of feet by 12

What are the formulas for the perimeter and area of an equilateral triangle?

Perimeter = 3s, Area = (s^2 * sqrt(3)) / 4, where s is the side length

How can trigonometric ratios be used to find the height of a triangle?

Use sine, cosine, or tangent based on the given angle and side.

What trigonometric function would you use to find the angle?

With sides known, use inverse trigonometric functions (arcsin, arccos, arctan) to calculate the angle.

When do you use the Law of Cosines?

Use the Law of Cosines when you know two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

How do transformations affect the sine function?

Vertical stretch affects amplitude, horizontal translation shifts the graph left/right, vertical translation shifts the graph up/down, and reflection flips the graph over the x-axis.

What is the effect of parameter values on a sine graph?

Changing the parameter inside the sine function affects the period (horizontal stretch/compression).

What is a domain restriction?

The set of input values for which a function is defined.

What are the components of a trigonometric function?

Domain, range, asymptotes describe the behavior of the function.

sin(90-x)=?

cos(x)

How do you solve unknown sides/angles of triangles?

Use the Law of Sines or the Law of Cosines as appropriate based on the given information.

What type of functions can model average monthly temperatures over time?

Sinusoidal functions

How do you model sinusoidal motion?

Use a sine or cosine function with appropriate amplitude, period, and phase shift.

What determines amplitude?

The distance between the relative minimum and maximum is twice the amplitude.

How is a sinusoidal function structured?

h(t) = A cos(B(t - C)) + D, where A is amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

What different functions can respresent a sinusoidal function?

Sine and cosine functions with appropriate amplitude, period, and phase shift, can all represent the same sinusoidal function.

Are harmonic pulse measurements periodic?

Yes, this is due to their periodic relationship with the unit circle.

What are the formulas for circular motion?

θ = arc length/radius, ω = θ/time, v = radius * ω

How are angular velocity and linear velocity related?

linear velocity = radius * angular velocity

What are inverse trigonometric functions?

Inverse trigonometric functions are the inverse functions of the trigonometric functions.

What are equivalent expressions for cot θ?

cot θ = cos θ / sin θ = 1 / tan θ

What is the simplified form of (sin^2 θ) / (1 - cos θ)?

1 + cos θ