3B Review (3.10-3.15)

Trig Equations and Inequalities

100

Solve the equation for [0, 2pi]. Find exact values.

4cos²x - 2cosx = 0

x = pi/3, pi/2, 3pi/2, and 5pi/3

200

Solve the equation for [0, 2pi]. Find exact values.

6sinx = 3(sqrt3)

x = pi/3 and 2pi/3

300

Solve the equation. Find ALL exact value(s).

4sin²x - 1 =1

x = pi/4 + (pi)n, 3pi/4 + (pi)n where n is an integer

or

x = pi/4 + (pi/2)n where n is an integer

400

Solve the inequality for [0, 2pi]. Find exact value(s).

2sinx + 2 < 1

(7pi/6, 11pi/6) or 7pi/6 <= x <= 11pi/6

500

Solve the inequality for [0, 2pi]. Find exact value(s).

2cosx + 3 >= 2

[0, 2pi/3] [4pi/3, 2pi]

Secant, Cosecant, Cotangent

100

Evaluate:

sec(5pi/6)

csc(pi)

cot(11pi/6)

-2(sqrt3)/3

undeefined

-(sqrt3)

200

What is the range for f(x) = csc(x)?

What is the range for f(x) = sec(x)?

What is the range for f(x) = cot(x)?

(-inf, -1] U [1, inf)

(-inf, -1] U [1, inf)

all reals

300

State the range and vertical asymptotes.

f(x) = 2csc(x - pi) - 1

range: (-inf, -3] U [1, inf)

x = (pi)n where n is an integer

400

State the range and vertical asymptotes.

f(x) = 3sec(1/2 x) + 1

range: (-inf, -2] U [4, inf)

x = pi + (2pi)n where n is an integer

500

State the range and vertical asymptotes.

f(x)= cot (2x)

range: all reals

x = (pi/2)n where n is an integer

Equivalent Rep. of Trig Functions

100

Use trig identities to write each expression in terms of a single trig identity.

sinx csx²x

csc x

200

Use trig identities to write each expression in terms of a single trig identity.

sin²x + cos²x + tan²x

sec²x

300

Use trig identities to solve the trig equation for [0, 2pi].

cos²x - 1 = sinx

x = 0, pi/2, pi, 2pi

400

Find the exact value.

cos(3pi/2 + 4pi/3)

-(sqrt3)/2

500

Use trig identities to solve the trig equation for [0, 2pi].

cos(2x) = cos²x

x = pi/2, 7pi/6, 3pi/2, 11pi/6

Trig and Polar Coordinates

100

Covert the polar coordinates to rectangular coordinates.

(8, 2pi/3)

(-4, 4(sqrt3) )

200

Covert the polar coordinates to rectangular coordinates.

(-2, pi/4)

( -(sqrt2), -(sqrt2) )

300

Convert the rectangular coordinates to polar coordinantes where 0 <= theta <= 2pi

(-3, 6)

( 3(sqrt5), 2.034)

400

Convert rectangular complex numbers to polar form.

-6 + 4i

2(sqrt13) [cos(2.553) + i sin(2.553)]

500

Convert polar complex numbers to rectangular form.

6 [cos(5pi/4) + i sin(5pi/5)]

-3(sqrt2) + 3i(sqrt2)

Polar Function Graphs

100

if n is odd, how many petals will there be?

if n is even, how many petals where there be?

n petals

2n petals

200

a cardioid limacon occurs when a ___ b

a dimpled cardioid occurs when a ___ b

an inner loop limacon occurs when a ___ b

a = b

a > b

a < b

300

Use the polar function below and determine the type of polar graph as well as the endpoints of [pi/2, 2pi/3]

r = 5cos(2theta)

rose with 4 petals

endpoints: (-5, pi/2) (-5/2, 2pi/3)

400

Look at the table and determine the interval(s) where f is increasing and where f is decreasing.

increasing: (0, 3pi/4) and (5pi/4, 2pi)

decreasing: (3pi/4, 5pi/4)

500

Look at the table and find the average rate of change between theta = pi and theta = 5pi/4

33.24/-pi ~ -10.58 units per radian