Victory for the ACT Student Text 15e

248 • M ATH

GRAPHS OF TRIGONOMETRIC FUNCTIONS

Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ †‘‡• …‘””‡…–Ž› †‡•…”‹„‡ –Š‡ ‰”ƒ’Š ‘ˆ ( ) 2 1 sin ( ) f x x = + r ‹ –Š‡ •–ƒ†ƒ”† ȋ x,y Ȍ…‘‘”†‹ƒ–‡ ’Žƒ‡ǫ A. ( ) f x Šƒ• ŠƒŽˆ –Š‡ ƒ’Ž‹–—†‡ ‘ˆ ( ) sin g x x B. ( ) f x Šƒ• ŠƒŽˆ –Š‡ ƒ’Ž‹–—†‡ ‘ˆ ( ) sin ( ) g x x + r = Ǥ ( ) f x ‹• •Š‹ˆ–‡† –‘ –Š‡ Ž‡ˆ– ‘ˆ ( ) sin g x x 2 1 „› r D. ( ) f x ‹• ‹†‡–‹…ƒŽ –‘ ( ) 2 1 sin ( ) g x x = − r

Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‡“—ƒ–‹‘• ‹• ‡“—ƒŽ –‘ –Š‡ ˆ—…–‹‘ ‰”ƒ’Š‡† „‡Ž‘™ǫ y

11.

12.

Throwback to Math Š‡ ‰‡‡”ƒŽ ˆ‘” ˆ‘” –Š‡ ‡“—ƒ–‹‘ ‘ˆ ƒ –”‹‰‘‘‡–”› ˆ—…–‹‘ ‹•ǣ [ ( )] y Af B x C D = + + ™Š‡”‡ f ‹• –Š‡ –”‹‰‘‘‡–”› ˆ—…–‹‘ǡ A ‹• –Š‡ ƒ’Ž‹–—†‡ǡ B

4

2

–2π –3π/2 –π –π/2

π/2 π 3π/2 2π

0

x

F. sin 2 G. cos x 2 H. sin 1 2 x

Ǥ ( ) f x g x Š‡Ž’• †‡–‡”‹‡ –Š‡ ’‡”‹‘†ǡ C ‹• –Š‡ •Š‹ˆ– Ž‡ˆ– ȋ Ȍ ‘” ”‹‰Š– ȋ Ȍǡ ƒ† D ‹• –Š‡ •Š‹ˆ– —’ ȋ Ȍ ‘” †‘™ ȋ ). Throwback to Math Class ‘— •Š‘—Ž† „‡ ˆƒ‹Ž‹ƒ” ™‹–Š –Š‡ ‰”ƒ’Š• ‘ˆ –Š‡ •‹‡ ˆ—…–‹‘ ƒ† –Š‡ …‘•‹‡ ˆ—…–‹‘Ǥ y ‹• •Š‹ˆ–‡† —’ ˆ”‘ x 1 ( ) sin 2 „› r

J. K.

x 1 2

x

cos

2

x

1 2

cos

2

cos x

1

sin x

x

0

–1

–2

–2π

–3π/2 –π –π/2

π/2 π 3π/2 2π

‡‡„‡”ǡ –Š‡ ƒ’Ž‹–—†‡ ‹• –Š‡ ƒš‹— Š‡‹‰Š– ‘ˆ –Š‡ ˆ—…–‹‘ ˆ”‘ –Š‡ x Ǧƒš‹• ȋ™Š‹…Š ‹• ŠƒŽˆ –Š‡ –‘–ƒŽ ”ƒ‰‡Ȍ ƒ† –Š‡ ’‡”‹‘† ‹• –Š‡ †‹•–ƒ…‡ ‘ –Š‡ x Ǧƒš‹• ‘˜‡” ™Š‹…Š –Š‡ ˆ—…–‹‘ ”‡’‡ƒ–•Ǥ –360ሞ –270ሞ –180ሞ –90ሞ 90ሞ 180ሞ 270ሞ 360ሞ