MHF4UA Unit5 RMc jggm tujrtj jbjrhtg ryh PDF

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Unit 5 Assessment Task 1: Knowledge/Understanding 1. Determine SA for each negative angle: a. -98◦

SA=180 0−980 ¿ 820 −π 3

b.

SA=π −

π 3

2π 3 cot θ=1.6 for domain 0 ≤θ ≤ 360 °. Round to nearest degree. ¿

2.

cot θ=1.6 1 =1.6 tan θ 1 tan θ= 1.6 5 ¿ 8 1st quadrant

tan θ=

5 8

θ=tan−1

( 58 )

¿ 32° 2nd quadrant

SA =180 ° +32 ° ¿ 212° 3. Use unit circle to evaluate these trig ratios a. b. c.

y 1 sin 90 °= = =1 r 1 x −1 cos π= = =−1 1 r 3π r 1 1 = = =−1 = csc sin θ y −1 2

( )

4. Convert from degrees to radians. Leave answers in exact from.

220 °→ 220° ×

a.

π 180 °

48 ° → 48° ×

b.

=

220 π ° 11 π = 9 180 °

π 48 π ° 4 π = = 180 ° 180 ° 15

5. Convert from radians to degrees. Round to nearest degree (ND). a.

3 π 180 ° 540 ° 3π = × → =135 ° π 4 4 4

b.

1.5 →

1.5 180 ° 270° = = =86° π 1 π

6. Determine the related acute angle (RA) for

SA=

7 π 180 ° × =105° 12 π

SA =180 °− RA ∴ RA =180 °−105 ° ¿ 75 ° 7. Determine the exact value:

a.

tan

( 56π )

SA=

5 π 180° =150 ° × π 6

SA =180 °− RA ∴ RA =180 °−150 ° ¿ 30 ° 5π Now→−tan =−0.577 6

( )

b.

cos

( 74π )

SA=

7 π 180 ° × =315° 4 π

SA=360 °−RA ° ∴ RA =180 °−315 ° ¿ 45 °

7π . Which quadrant does it lie? 12

cos

7π =0.7071 4

( )

8. Map (0,1) on the graph of

y=cos x onto the graph of

y=3 cos ( x−5 )+ 11 .

a =3, k=1, d =5, c=11

[

]

1 ( x ) +d , a ( y )+c k 1 (0,1 )→ ⌊ ( 0) +5 , 3 ( 1) +11 ⌋ 1 →( 5,14 ) (x , y )→

Task 2: Thinking 9. SA for point (-8,-6). Round to nearest degree.

y −6 3 = tan θ= = x −8 4 θ=tan−1

( 34 )

¿ 37 °(nd) SA =180 ° + RA ¿ 180° +37 ° ¿ 217 °

y=tan θ and its reciprocal for the interval −2 π ≤ θ ≤ 2 π . List the special features 1 wave, vertical asymptote (VA), domain, and range for for each graph. Include the period, 4

10. Draw

this interval.

θ

Vertical Asymptote

x=

π 2

π 3π x 2= +π= 2 2 x 3=

3 π π 5π + = 2 2 2

Range

sin x cos x range: (−∞ , ∞ ) recall: tan θ=

x- intercepts intervals located wherever

x=0, π , 2 π Features    

Period = 2 π

π 1 wave= 4 4 π 3π , , VA → x= , x= 2 2 Domain→−2 π ≤ θ ≤ 2 π

sin x =0 cos x



Range→−∞ , ∞

11. Determine the exact value using compound-angle formula:

a.

( 116π ) =cos 2 π cos 6π +sin2 π sin π6 1 √3 ¿ ( 1 ) ( )+( 0 ) ( ) 2 2 cos

¿

√3 2

12. Simplify:

( π2) =cos x cos 2π −sin x sin π2

cos x+

¿ cos x ( 0)−sin x (1 ) ¿−sin x 13. If

cos x=

12 , where 0< x...