Precalculus 1-2 Terms

Precalculus Terms

Unit Circle

Can be measured in degree or radians, four quadrants, used to measure angles, etc.

Trigonometry

relationship between the sides of a triangle (right triangle) with its angles. There are six functions of an angle commonly used in trigonometry:

Initial Ray

the starting point of an angle in standard position, extending from the origin along the positive x-axis.

Terminal ray

the ray that represents the angle's endpoint, extending from the vertex of the angle and determining the angle's measure.

Vertex

the point where the two rays of an angle meet, forming the angle.

Sine

a trigonometric function defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. (opposite/ hypotenuse)

Cosine

a trigonometric function defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. (adjacent/hypotenuse)

Tangent

a trigonometric function defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. (opposite/adjacent)

Secant

a trigonometric function defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right triangle. (hypotenuse/adjacent)

Cosecant

a trigonometric function defined as the ratio of the length of the hypotenuse to the length of the opposite side in a right triangle. (hypotenuse/opposite)

Cotangent

The ratio of the adjacent side to the opposite side in a right triangle, or the reciprocal of the tangent function. (adjacent/ opposite)

Arc Length Formula

The formula used to determine the length of an arc of a circle, calculated as the product of the radius and the central angle in radians. (Length = radius × angle)

Sector Area Formula

The formula used to calculate the area of a sector of a circle, determined by the product of one-half the radius squared and the central angle in radians. (Area = 1/2 × radius² × angle)

Reference Angles

The acute angle created by the terminal ray and the x-axis based on quadrant location.

Pythagorean Theorem Formula

A mathematical equation stating that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. (a² + b² = c²)

Exact Value

The value of a trigonometric function at a specific angle that can be expressed as a simple fraction or whole number, often found for commonly used angles such as 0°, 30°, 45°, 60°, and 90°. To find this, convert to degrees and plug directly into formula.

Using Given information to find a trig value

Identify the trig ratio, create a diagram, and use the Pythagorean theorem to find the missing side.

Polar Coordinates

In order to solve this, you need to find the cos and sin coordinates. This means that you will use the following formula to solve for the missing variable coordinate: x²+y²= 1 (don’t forget to take the square root! answers should be fractions)

Terminal Number

subtract 2 pie from value

Periodic Graphs

Sine and Cosine graphs that repeat every 2π. They contain amplitude, phase shift, midline, and period.

Sin Graph Formula

y= A sin(B(x+c))+d

Cos Graph Formula

y= A Cos (B(x+c))+d

Amplitude

Absolute value (max - min / 2)

Midline

represented by d (max + min / 2)

Period

2π/b

Phase shift

Frequency

b/2π (flip the period)

Law of sines (AAS)

SinA/ a = SinB/b = SinC/ c

(Set the missing side equal to the known side)

Law of Sines (SSA)

SinA/ a = SinB/b = SinC/ c

(solving for 1 angle and 1 side)

-cross multiply and take inverse

Law of Cosines (Sides)

take square root

Law of Cosines (Angles)

take inverse