Pre Cal Terminology

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Theta, Beta, Alpha- A variable used in trigonometry usually for unknown angles.

Angle of depression: An angle you can slide down

Angle of elevation: An angle you cant slide down

Bearing: Never Eat Soggy Waffles problems

Tangent: Tangent can equal a point that touches a circle

Co-terminal angle: Two angles are co-terminal if they end at the same place on the unit circle.

Standard Position:
Quadrants Rule:

$\pi$ = Equal to 180

Reference angle:

Reference angle theorem:

Reciprocal Identities:

Acute angle- Angle less than 90 degrees.

Right angle- exactly 90 degrees.

Obtuse angle- Angle between 180 degrees and 90 degrees.

Straight Angle- exactly 180 degrees and basically a line.

Complementary Angles- Add up to 90 degrees

Supplementary Angles- Add to 180

Parallel Lines - Lines that never intersect

Transversal line- A line that intersects parallel lines

Types of triangles

Isosceles Triangles

• 2 same sided lines while one remains different.

• 2 angles with the same measurements

• plus line of symmetry down the middle

Equilateral triangles:

• all sides are the same length.

• has symmetry (can be split equally more than once)

Scalene triangle:

• 3 different side lengths

• 3 different angles

• no lines of symmetry (cannot be spilt equally)

30-60-90 & 45-45-90 Triangles

    45-45-90

• Its an isosceles triangle

• It has two legs that are congruent like the 45 degree angles

• Its special because the third angles needs the x of the two congruent legs to be solved

  
  

  

    30-60-90

• The position of the angles is relevant to the sides.

• Across the angle 30 is the shortest side of the triangle.

• Across the angle 90 is the hyp / Longest angle.

• Across the 60 is the longer angle.

  
  

  Why is the positions of these angles relevant? - Because these sides have specific plug ins for each.

• 30 = x

• 60 = (x)√3

• 90 = 2(x)

  
  

  

“What can i use this for?”

You can use the 30-60-90 AND 45-45-90 to find Soh Cah Toa with only the degrees.

Ex. Sin 60 degrees using the 30-60-90 is √3/2. Solve like a regular Sin 60 using Soh Cah Toa then rationalize the x out of the fraction.

Same can be done with the 45-45-90.

Additional Method “finger method”

Parallel and Transversal angles

Law of sines and law of cosines

“What is law of sines and cosines?” - Law of sines and cosines is the formulas used to find

Law of sines:

• one of the sines has to be fully solved in order to find the variable on the other side

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Triangle congruence theorems

Definition: The triangle congruence theorems tells me two shapes are similar by these rules.

ASA: Two angles and the included side are congruent.

SSS: All three sides are congruent.

AAS: Two angles and a non-included side are congruent.

SAS: Two sides and the included angle are congruent.

HL: The hyp and one of the legs are congruent.

Formulas

Cofunction identities

• sin θ = cos( 90 - θ )

• tan θ = cot( 90 - θ )

• sec θ = csc( 90 - θ )

  
  

  
  

missing sides of similar triangles

left triangle side A / right triangle side A = left triangle side B / right triangle side B

Reference angle theorem

Exact Values

Key Lesson Concepts

8/21/25

Definitions:

• Standard Position:

  
  

“ALL STUDENTS TAKE CALCULUS”

• Method of finding which of Sin Cos and Tan are positive in their quadrants

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8/26/25

Reference angle:

Reference angle theorem:

Reciprocal Identities: