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Understanding Pythagorean identities

CC.HSF.TF.A.1

Converting between degrees and radians

Trigonometric ratios of angles in radians

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Radian measure and arc length

CC.HSF.TF.A.2

Unit circle

CC.HSF.TF.A.3

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Find the exact value of trigonometric ratios

CC.HSF.TF.B.5

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

CC.HSF.TF.B.6

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

CC.HSF.TF.B.7

Evaluating inverse trigonometric functions

CC.HSF.TF.C.8

Pythagorean identities

CC.HSF.TF.C.9

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

CC.HSG.C.B.5

CC.HSG.CO.A.1

Line symmetry

Angles in a circle

Chord properties

Circles and circumference

Circle properties

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

CC.HSG.SRT.C.6

Use sine ratio to calculate angles and sides (Sin = o / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

CC.HSG.SRT.C.7

Use cosine ratio to calculate angles and sides (Cos = a / h)

CC.HSG.SRT.C.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

CC.HSG.SRT.D.10

Law of sines

Ambiguous case: SSA triangles

Law of cosines

CC.HSG.SRT.D.11

Applications of the sine law and cosine law

CC.HSG.SRT.D.9

Area of triangles: 1/2 a*b sin(C)

CC Standards Trigonometry

sample

math

Ex. 1:

Proving all three Pythagorean identities using the unit circle

Ex. 2:

Ex. 3

Simplifying secant squared minus one times cotangent squared

Proving sinx/(1+cosx) + sinx/(1-cosx) = 2cscx

Simplifying a trig expression using conjugates and Pythagorean identities

Proving tanx(cscx+1) equals cotx/(cscx-1) using conjugates

Pythagorean identities are formulas, derived from Pythagorean Theorem, that allow us to find out where a point is on the unit circle. Learn the tricks and tips on how to use the unit circle to derive and prove the Pythagorean identities can be difficult. 

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

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

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