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Find the Exact Value of Trigonometric Ratios

NL.SO.2200AN2

Conversion between entire radicals and mixed radicals

auto-gen

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Dividing radicals

Rationalize the denominator

NL.SO.2200AN3

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

NL.SO.2200AN4

Partial fraction decomposition

Simplifying rational expressions and restrictions

NL.SO.2200AN5

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

NL.SO.2200AN6

Solving rational equations

Applications of rational equations

NL.SO.2200RF1

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

NL.SO.2200RF10

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

NL.SO.2200RF11

Graphing reciprocals of linear functions

Sigma notation

Graphing reciprocals of quadratic functions

NL.SO.2200RF2

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

NL.SO.2200RF3

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

NL.SO.2200RF4

Applications of quadratic functions

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Completing the square

Completing the Square

NL.SO.2200RF5

Solving polynomial equations by iteration

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

NL.SO.2200RF6

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

NL.SO.2200RF7

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

NL.SO.2200RF8

Solving quadratic inequalities

NL.SO.2200RF9

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Graphing systems of linear inequalities

Applications of inequalities

NL.SO.2200T1

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

NL.SO.2200T2

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NL.SO.2200T3

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Parent Assignments

Challenge Zone

Foundation Review

Advanced Mathematics 2200

Algebra and Number

Relations and Functions

math

Ex. 1:

Evaluating six trig ratios for 30 degrees using special triangles

Evaluating all six trig ratios for 120 degrees

Evaluating all six trig ratios for 225 degrees

Trig ratios for 300 degrees and signs in quadrant four

This lesson shows how to find exact values of trigonometric ratios for special angles like 30, 45, 60, and 90 degrees, using right triangle ratios, the unit circle, and reference angles, with worked examples in degrees and radians.

Solving expressions using 45-45-90 special right triangles 

Solving expressions using 30-60-90 special right triangles 

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Overview

Find the Exact Value of Trigonometric Ratios

What You'll Learn

Exact trig values are written as fractions and radicals, such as one half or square root of two over two, instead of rounded decimals.

The 30 degree, 45 degree, and 60 degree angles come from two special right triangles whose side ratios never change.

The unit circle extends these exact values to every quadrant using coordinates equal to cosine and sine.

A reference angle plus the ASTC rule tells you the correct exact value and sign for any angle, in degrees or radians.

Worked examples walk through finding exact values for angles like 150 degrees and 225 degrees step by step.

What You'll Practice

Finding exact trigonometric values for angles like 30°, 60°, 120°, 225°, and 300°

Drawing standard position angles and identifying the correct reference angle

Calculating reciprocal ratios (cosecant, secant, cotangent) from primary ratios

Determining which trigonometric functions are positive in each quadrant

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

4 Video lessons

Practice exercises

Learning resources

Skills

Special Triangles

Reference Angles

SOHCAHTOA

Trigonometric Ratios

Reciprocal Functions

Quadrant Analysis

Exact Values