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How to use double-angle identities

Demonstrate understanding of effects of horizontal and vertical translations on graphs of functions and related equations

Combining transformations of functions

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Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Demonstrate understanding of product, quotient and power laws of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solve problems involving exponential and logarithmic equations

Solving logarithmic equations

Solving exponential equations with logarithms

Product rule of logarithms

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Solving exponential equations using exponent rules

Demonstrate understanding of effects of horizontal and vertical stretches on graphs of functions and related equations

Graphing reciprocals of linear functions

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Apply translations and stretches to graphs and equations of functions

Graphs of rational functions

Graphing reciprocals of quadratic functions

Demonstrate understanding of effects of reflections on graphs of functions and related equations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Even and odd functions

Demonstrate understanding of inverses of relations

One to one functions

Inverse functions

Graph and analyze radical functions involving one radical

Radical functions and transformations

Square root of a function

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Basic radical functions

Basic Radical Function

Basic Radical Functions

Demonstrate understanding of exponential functions

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Demonstrate understanding of logarithms

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

Converting from exponential form to logarithmic form

Graph and analyze exponential and logarithmic functions

Graphing logarithmic functions

Finding a logarithmic function given its graph

Demonstrate understanding of angles in standard position, expressed in degrees and radians

Angle in standard position

Coterminal angles

Coterminal Angles

Converting between degrees and radians

Develop and apply the equation of the unit circle

Unit circle

Reference angle

Find the exact value of trigonometric ratios

Solve problems using six trigonometric ratios for angles expressed in radians and degrees

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Trigonometric ratios of angles in radians

Radian measure and arc length

Graph and analyze trigonometric functions sine, cosine and tangent to solve problems

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

Solve first and second degree trigonometric equations algebraically and graphically

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

Prove trigonometric identities using various techniques

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

Pre-Calculus A 120

Relations and Functions

math

Ex. 1:

Ex. 2:

Ex. 3:

Finding sin 2A, sec 2A, and tan 2A given tangent and quadrant

Simplifying 14 sin(6x)cos(6x) using the sine double-angle identity

Simplifying cos(9/2 x) sin(9/2 x) using the sine double-angle identity

Simplifying cos²(5a) − sin²(5a) using the double-angle identity

Simplifying 3 minus 6 cosine squared using the double-angle identity

Simplifying 6tan(5x) over tan²(5x)−1 using the double-angle identity

Proving sin(6x)/(1+cos(6x)) = tan(3x) using double-angle identities

Proving a double-angle identity by starting from the right side

Proving a double-angle identity by simplifying sin4x and cos4x to tan x

Proving a double-angle identity by simplifying both sides to cotangent

In this lesson, we will learn how to make use of the double-angle identities, a.k.a. double-angle formulas to find the sine and cosine of a double angle. It's hard to simplify complex trigonometric functions without these formulas. 

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

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

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