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Angle and absolute value of complex numbers

Trigonometry: Master Angles, Functions & Applications

Imaginary and Complex Numbers

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Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Complex Conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Inverse Trigonometric Functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Finding exact value of inverse reciprocal trig functions

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

Inverse reciprocal trigonometric function: finding the exact value

Bearings

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Trigonometric Ratios and Angle Measure

Unit circle

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

ASTC rule in trigonometry (All Students Take Calculus)

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Graphing Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Applications of Trigonometric Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

Solving Trigonometric Equations

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Determining non-permissible values for trig expressions

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using Pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Right Triangle Trigonometry

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles 

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )

Our Trigonometry tutors have you covered with our complete trig help for all topics that you would expect in any typical Trigonometry classes, whether it&apos;s <a href="http://www.nysedregents.org/a2trig/home.html">Trigonometry Regents exam (EngageNY)</a>, <a href="http://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html">ACT Trigonometry</a>, or College Trigonometry. Learn trig with ease!

Our online trigonometry tutorials walk you through all topics in trigonometry like the Unit Circle, Trigonometric Identities, Trigonometric functions, Right triangle trigonometry, Trigonometric equations, and so much more. Learn the concepts with our trig tutorials that show you step-by-step solutions to even the hardest trigonometry problems. Then, reinforce your understanding with tons of trigonometry practice. 

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Ex.1

Ex.2

Ex.3

Converting a complex number from polar form to rectangular form

Finding the absolute value of a complex number using the Pythagorean theorem

Finding the angle of complex number z = 2 + 3i using inverse tangent

Finding the modulus of a complex number with rearranged terms

Finding the argument of a complex number using inverse tangent

There are times when we are interested in obtaining a better understanding of the properties of a complex number, such as its argument and modulus. In this section, we will learn how to calculate the argument, also known as the angle, and the modulus, also known as the magnitude or the <a href='[[glossary.html|{"keyword":"Absolute Value","term":"Absolute Value"}]]'>absolute value</a>, of a complex number.

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Solving expressions using 45-45-90 special right triangles 

Angle and absolute value of complex numbers

What You'll Learn

Calculate the modulus (absolute value) of a complex number using the Pythagorean theorem

Apply the formula |z| = (a² + b²) to find the magnitude of complex numbers

Determine the argument (angle) of a complex number using inverse tangent

Convert between polar and rectangular forms of complex numbers

Use trigonometric ratios to find real and imaginary parts from angle and magnitude

What You'll Practice

Finding the absolute value of complex numbers with positive and negative components

Calculating angles in radians using tan¹(b/a)

Converting complex numbers from polar form to rectangular form a + bi

Using special triangles to evaluate trigonometric expressions

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

5 Video lessons

Practice exercises

Skills

Complex Numbers

Modulus

Argument

Absolute Value

Polar Form

Rectangular Form

Trigonometry

Pythagorean Theorem