Victory for the ACT Student Text 15e

L ESSON 5 | T RIGONOMETRY • 245

LESSON 5 Trigonometry DEFINITIONS OF THE SIX TRIGONOMETRIC FUNCTIONS

Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‹• ‡“—‹˜ƒŽ‡– –‘ cos sin

‘” –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ sin ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‹• ǫ A. cos 13 5 i B. tan 5 12 i Ǥ cot 12 5 i D. sec 5 13 i Ǥ csc 13 12 i  –Š‡ ”‹‰Š– –”‹ƒ‰Ž‡ „‡Ž‘™ǡ –Š‡ Ž‡‰–Š ‘ˆ AB ‹• ͷ…‡–‹‡–‡”• ƒ† A + ‡ƒ•—”‡• ͵ͲιǤ Šƒ– ‹• –Š‡ Ž‡‰–Šǡ ‹…‡–‹‡–‡”•ǡ of BC ǫ ȋ sin30 2 1 c ) 13 12 i Ǥ Š‹…Š

A A ǫ A. tan B. cot Ǥ sec D. csc

3.

1.

The Cambridge Edge Š‡ ‡‘‹… Ǧ Ǧ …ƒ „‡ —•‡† –‘ ”‡‡„‡” –Š‡ †‡ϐ‹‹–‹‘• ‘ˆ •‹‡ǡ…‘•‹‡ǡ ƒ† –ƒ‰‡–Ǥ ǣ Sin i side Opposite

A A A

A Ǥ tan A 1

•‹šǦˆ‘‘–Ǧ–ƒŽŽ •—”˜‡›‘” ‹• •–ƒ†‹‰ ‘ –Š‡ ‰”‘—† ʹͲ͹ ˆ‡‡– ˆ”‘ –Š‡ „ƒ•‡ ‘ˆ ƒ „—‹Ž†‹‰ ͳǡ͹͹͸ ˆ‡‡– –ƒŽŽǤ Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‡š’”‡••‹‘• ‰‹˜‡• –Š‡ ƒ‰Ž‡ ‘ˆ ‡Ž‡˜ƒ–‹‘ ˆ”‘ –Š‡ –‘’ ‘ˆ –Š‡ •—”˜‡›‘”ǯ• Š‡ƒ† –‘ –Š‡ –‘’ ‘ˆ –Š‡ „—‹Ž†‹‰ǫ F. cot , 207 1 770 c m G. tan , 207 1 776 c m H. sin ,1 770 207 1 d n J. cos ,1 776 207 1 d n K. tan , 207 1 770 1 c m

4.

i

ǣ

Hypotenuse

i

Cos

2.

i

side Adjacent

ǣ

Hypotenuse

i

cos sin

i

Tan

i

i

side opposite

hypotenuse

i

side adjacent

hypotenuse

i i

side Opposite

F. 4 G. 3 H. 2 J. 2 2 1 K. 2 2 1 4 3

side Adjacent