IB SL I/Intens Precalc - Chapter 10 Review No Calculator

1. Given ( ) 3cos4

x- = and tan 0x < , use trig identities to find the values of the six trig functions.

2. Write a sine equation for the graph below in the form f x( ) = asin(bx − c)+ d , where a ,b, c, and d are all positive.

3. Sketch the following functions on the window [ ]2 ,2p p- .

a) 1sin2 4

y x pæ ö= - +ç ÷è ø

b) ( )3cosy xp= c) 4 tan 2y x= -

4. Find all solutions in the interval [ ]0,3p : ln sin 0x = 5. Evaluate each of the following:

a) 1 3sin2

- æ ö-ç ÷ç ÷è ø

b) 1 1tan3

- æ öç ÷è ø

6. Write an algebraic expression in terms of x, where 0x < , for ( )( )csc arccos 2 3x-

7. Write an algebraic expression in terms of x, where 0x > , for ( )sin 2arcsin x 8. Find the exact value of each of the following:

a) 13sin12p b) sec165

9. Find sinq if 5csc24

q =

10. Solve for 0 < x < 6π 8+ 6cos

θ3+ 2π

3⎛⎝⎜

⎞⎠⎟= 3 2 +8

Calculator Allowed 11. Verify each identity

a) cos sin coscos1 tan cos sin

q q qqq q q- =

- -

b) 1 5

32 2sin cos sin cos cos sinx x x x x x- = c) ( ) ( )sin sin 2sin cosx y x y x y+ + - =

d) csccsc22cos

aaa

=

e) 4 4cos sin cos2x x x- = 12. Solve each equation on the interval [ ],p p-

a) cos cos 14 4

x xp pæ ö æ ö+ - - =ç ÷ ç ÷è ø è ø

b) 4sin cos 1x x =

15. Given 2cos ,7 2

u up p= - < < find the exact values of sin 2 ,cos2 , tan 2u u u

16. Rewrite the expression in terms of the first powers of cosine: 2 2sin cosx x

ANSWER KEY 1.

7 4 7sin csc4 7

3 4cos sec4 37 3 7tan cot3 7

x x

x x

x x

= - = -

= =

= - = -

2. f x( ) = 2sin 2

3x − 2π⎛

⎝⎜⎞⎠⎟+ 3

3. a)

-3π/2 -π -π/2 π/2 π 3π/2

-5-4-3-2-1

12345

x

y

b) Note: The period of this one is 2. So key points at 1 30, ,1, ,22 2

-3π/2 -π -π/2 π/2 π 3π/2

-5-4-3-2-1

12345

x

y

c)

-3π/2 -π -π/2 π/2 π 3π/2

-5-4-3-2-1

12345

x

y

4. 3 5, ,2 2 2

x p p p=

5. a) 3p

- b) 6p

6. 2

14 12 8x x- + -

7. 22 1x x-

8. a)

6 24

- + b) 42 6

-+

9. 55

10. x = 13π

4,19π

4

11. Yup, they work

12. a) 3,4 4

x p p= - - b) 5 7 11, , ,

12 12 12 12x p p p p= - -

13. 12 5 41 12 5sin 2 cos2 tan 249 49 41

u u u= - = - =

14. 1 1cos48 8

x- +