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  1. AP Pre Calculus
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What is the formula for tangent (tan θ)?

tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}tan(θ)=cos(θ)sin(θ)​

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What is the formula for tangent (tan θ)?

tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}tan(θ)=cos(θ)sin(θ)​

What is the relationship between degrees and radians?

π radians=180∘\pi \text{ radians} = 180^{\circ}π radians=180∘

What are the coordinates of point P on the unit circle?

P=(cos⁡(θ),sin⁡(θ))P = (\cos(\theta), \sin(\theta))P=(cos(θ),sin(θ))

SOHCAHTOA: What is the formula for Sine?

sin⁡(θ)=OppositeHypotenuse\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}sin(θ)=HypotenuseOpposite​

SOHCAHTOA: What is the formula for Cosine?

cos⁡(θ)=AdjacentHypotenuse\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}cos(θ)=HypotenuseAdjacent​

SOHCAHTOA: What is the formula for Tangent?

tan⁡(θ)=OppositeAdjacent\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}tan(θ)=AdjacentOpposite​

Formula to convert degrees to radians?

radians=degrees×π180\text{radians} = \text{degrees} \times \frac{\pi}{180}radians=degrees×180π​

Formula to convert radians to degrees?

degrees=radians×180π\text{degrees} = \text{radians} \times \frac{180}{\pi}degrees=radians×π180​

What is the formula relating x, y, and r on the unit circle?

x2+y2=r2x^2 + y^2 = r^2x2+y2=r2, and since r=1, x2+y2=1x^2 + y^2 = 1x2+y2=1

What is the general form for coterminal angles?

θ+2πk\theta + 2\pi kθ+2πk, where k is an integer.

What are the differences between sine and cosine functions?

Sine: y-coordinate on the unit circle, odd function | Cosine: x-coordinate on the unit circle, even function

What are the differences between positive and negative angles on the unit circle?

Positive angles: Measured counterclockwise | Negative angles: Measured clockwise

What are the differences between radians and degrees?

Radians: Based on the radius of the circle, dimensionless | Degrees: Arbitrary division of a circle into 360 parts

Compare sin(θ) and cos(θ) at θ = 0.

sin(0) = 0 | cos(0) = 1

Compare sin(θ) and cos(θ) at θ = π/2.

sin(π/2) = 1 | cos(π/2) = 0

Compare the range of sine and cosine functions.

Sine: [-1, 1] | Cosine: [-1, 1]

Compare the graphs of y = sin(x) and y = cos(x).

y = sin(x): Starts at (0, 0), odd function | y = cos(x): Starts at (0, 1), even function

Compare the derivatives of sin(x) and cos(x).

Derivative of sin(x): cos(x) | Derivative of cos(x): -sin(x)

Compare the integrals of sin(x) and cos(x).

Integral of sin(x): -cos(x) + C | Integral of cos(x): sin(x) + C

Compare the use of sine and cosine in right triangles.

Sine: Opposite/Hypotenuse | Cosine: Adjacent/Hypotenuse

What is the unit circle?

A circle with a radius of 1, centered at the origin (0,0).

What is an angle in standard position?

An angle that starts from the positive x-axis and goes counterclockwise.

Define 'radians'.

A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius.

Define 'terminal ray'.

A line from the origin at a given angle that intersects the unit circle.

Define sine (sin θ) in the context of the unit circle.

The y-coordinate of the point where the terminal ray intersects the unit circle.

Define cosine (cos θ) in the context of the unit circle.

The x-coordinate of the point where the terminal ray intersects the unit circle.

Define tangent (tan θ) in the context of the unit circle.

The ratio of the y-coordinate to the x-coordinate (sin θ / cos θ) of the point where the terminal ray intersects the unit circle.

What are reflex angles?

Angles greater than 180° but less than 360°.

What is a 'full rotation' in radians?

2π radians.

What is the ASTC rule?

A mnemonic to remember which trig functions are positive in each quadrant: All, Sine, Tangent, Cosine.