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Maths Extension 1 Trigonometry

Trigonometry

Trigonometric Ratios

Exact Values & Triangles

Trigonometric Identities ASTC Rule

Trigonometric Grahs

Sine & Cosine Rules

Area o! a Triangle

Trigonometric E"uations

Sums and #i!!erences o! angles

#ou$le Angles

Trile Angles %al! Angles

T !ormula

Su$sidiary Angle !ormula

General Solutions o! Trigonometric E"uations

Radians

Arcs Sectors Segments

Trigonometric 'imits

#i!!erentiation o! Trigonometric (unctions

Integration o! Trigonometric (unctions Integration o! sin)x and cos)x

I*VERSE TRIG*+METR,

In-erse Sin Grah #omain Range .roerties

In-erse Cos Grah #omain Range .roerties

In-erse Tan Grah #omain Range .roerties

#i!!erentiation o! In-erse Trigonometric (unctions Integration o! In-erse Trigonometric (unctions

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Maths Extension 1 Trigonometry

Trigonometric Ratios

Sine sin 3hypotenuse

opposite

Cosine cos 3hypotenuse

adjacent

Tangent tan 3adjacent

opposite

Cosecant cosec 3sin

13

opposite

hypotenuse

Secant sec 3 cos1

3 adjacenthypotenuse

Cotangent cot 3tan

13

opposite

adjacent

sin 3 ( )45cos

cos 3 ( )45sin

tan 3 ( )45cot

cosec 3 ( )45sec

sec 3 ( )45cosec

cot 3 ( )45tan

65 seconds 3 1 minute 6577 3 1765 minutes 3 1 degree 657 3 18

cos

sintan =

sin

coscot =

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9

9

hyotenuse

hyotenuse

oosite

ad2acent

ad2acent

oosite

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Maths Extension 1 Trigonometry

Exact Values & Triangles

58 :58 658 ;

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Maths Extension 1 Trigonometry

ASTC Rule

(irst >uadrant/ Allositi-esin sin ?cos cos ?tan tan ?

Second >uadrant/ Sine ositi-e

( )1=5sin sin ?( )1=5cos cos ( )1=5tan tan

Third >uadrant/ Tangent ositi-e( )+1=5sin sin ( )+1=5cos cos ( )+1=5tan tan ?

(ourth >uadrant/ Cosine ositi-e( ):65sin sin ( ):65cos cos ?( ):65tan tan

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:65

5

458

1=58

)@58

S A

T C

1st>uadrant

;th>uadrant

)nd>uadrant

:rd>uadrant

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Maths Extension 1 Trigonometry

Trigonometric Grahs

Sine & Cosine RulesSine Rule/

C

c

B

b

A

a

sinsinsin== +R

c

C

b

B

a

A sinsinsin==

Cosine Rule/Abccba cos)

))) +=

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