Precal Review

3/5

(12, 16); Find cos θ

-7/6

(7, -6); Find cot θ.

-81.33 degrees

-1.4194 radians

-π/3

-60 degrees

-36 degrees

-π/5

13π/6 radians

390 degrees

ø

3x^2 + 3y^2 = 20 6x^2 + 6y^2 = 48

0.7505 radians

43 degrees

circle

4x^2 = 16 - 4y^2

parabola

5x^2 - y = 8

450 degrees

5π/2

-3

9tan180degrees + 3csc270degrees

191 ft

A conservation officer needs to know the width of a river in order to set instruments correctly for a study of pollutants in the river. From point A, the conservation officer walks 110 feet downstream and sights point B on the opposite bank to determine that θ = 60° (see figure). How wide is the river (round to the nearest foot)?

30 ft

A guy wire to a tower makes a 71° angle with level ground. At a point 32 ft farther from the tower than the wire but on the same side of the base as the wire, the angle of elevation to the top of the pole is 34°. Find the wire length (to the nearest foot).

4

Amplitude of y = -4 cos 13 x

1

Factor the trigonometric expression and simplify. sin^2x + sin^2xcot^2x

an = 1/6(6)^n-1

Find a general term an for the geometric sequence. 1/6,1,6

27.9362472°

Find a value of θ in [0°, 90°] that satisfies the statement. cot θ = 1.8857855

45° and 225°

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value tan θ = 1

135° and 225°

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value secθ=- √2

60° and 120°

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value sinθ=√3/2

an = 4n-2 ; a6 = 22

Find an and a6 for the following arithmetic sequence. 2, 6, 10, 14, 18

√191/4

Find cos A when a = √5 and c = 14.

520 degrees and -200 degrees

Find positive and negative coterminal angles 160 degrees

4/5

Find sin A when b = 12 and c = 20

99°

Find the angle of least positive measure coterminal with the given angle. -261°

6.3 m^2

Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest tenth. r = 6.0 m, θ = 20°

11,433 m^2

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. a = 153 m b = 165 m c = 171 m

20.4 in.^2

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. A = 38.1° b = 12.0 in. c = 5.5 in.

C: (0,0) ; F: (√17,0), (√17,0); A: y = 4x, y = -4x

Find the center, foci, and asymptotes of the hyperbola. x^2 - y^2/16=1

(x - 5)^2 + y^2 = 9

Find the center-radius form of the circle described or graphed. a circle having a diameter with endpoints (5, -3) and (5, 3)

4

Find the common difference for the arithmetic sequence. 6, 10, 14, 18, . .

-3

Find the common ratio r for the given infinite geometric sequence. 3, -9, 27, -81, 243, . . .

52 deg

Find the complement of an angle whose measure is 38°.

<50, -38>

Find the component form of the indicated vector. Let u = 5, -1 , v = -7, 7 . Find 3u - 5v.

20

Find the dot product for the pair of vectors. 1, 17 , 3, 1

-1/2

Find the exact circular function value. cos-2pi/3

√3

Find the exact circular function value. cot -11π/6

a 1 = 21, d = 8

Find the first term and common difference a12 = 109, a68 = 557

-5/42 -1/7 1/21 -1/7

Find the inverse, if it exists, for the matrix -6 6 -2 -5

-3 10 -3 2 -4 1 -1 1 0

Find the inverse, if it exists, for the matrix 1 3 2 1 3 3 2 7 8

37.1 cm

Find the length of an arc intercepted by a central angle θ in a circle of radius r. Round your answer to 1 decimal place. r = 10.63 cm.; θ = 10/9 π radians

13; 157.4°

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. <-12,5>

10 ; 150°

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. <-5√3,5>

B = 23.3°, C = 62.2°, c = 34 ft

Find the missing parts of the triangle A = 94.5° b = 15.2 ft a = 38.3 ft If necessary, round angles and side lengths to the nearest tenth.

A = 18.6°, B = 21.4°, C = 140°

Find the missing parts of the triangle AB = 329 yd AC = 187 yd BC = 163 yd

c = 11.9 m, A = 21°, B = 40.8°

Find the missing parts of the triangle C = 118.2° a = 4.8 m b = 8.9 m

no such triangle

Find the missing parts of the triangle. A = 118.1° a=1229cm b = 1329 cm If necessary, round angles to the nearest tenth and side lengths to the nearest cm.

13, 122

Find the nth term of the geometric sequence 2, -6, 18, ... ; n = 9

7/ + 5/ 2x-7 3x-5

Find the partial fraction decomposition for the rational expression 31x-70/ 6x^2-31x+35

7/ + -1/ x + 3 x - 2

Find the partial fraction decomposition for the rational expression 6x-17/ (x+3)(x-2)

4π

Find the period of y = 5 sin(1/2x - π/2)

π/4 units to the right

Find the phase shift y = 4sin(2 x - π/2)

π/2 units to the right

Find the phase shift y = cos(x - π/2)

71°

Find the reference angle for the given angle 109°

12324

Find the sum of the first 78 positive multiples of 4.

450

Find the sum of the first n terms of the following arithmetic sequence a2 = -25, a5 = 35; n = 10

15

Find the sum. 9 + 18/5 + 36/25 + 72/125 + ...

91 deg

Find the supplement of an angle whose measure is 89°.

1.3552

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. tan s = 4.5653

down 3

Find the vertical translation of y = -3 + 2 sin (4x + π/2)

188° + n ∙ 360°

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 188°

(-2, 3), x = -2

Give the vertex and axis of symmetry for the parabola (x+2)^2 = -28(y-3)

91

If u = <-5, 7> , v = <4, 6> , and w = <-11, 2> , evaluate u ∙ (v + w)

30 m

On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

a = 3.9 mm, A = 57.3°, b = 2.5 mm

Solve the right triangle B = 32.7°, c = 4.6 mm, C = 90° Round values to one decimal place.

A = 66.8°, B = 23.2°, c = 3.8 cm

Solve the right triangle. a = 3.5 cm, b = 1.5 cm, C = 90° Round values to one decimal place.

A = 64.4°, a = 76.1, c = 83

Solve the triangle. B = 15.4° C = 100.2° b = 22.4

4, 20, 52

The weekly sales in thousands of items of a product has a seasonal sales record approximated by n = 85.94 + 25.1 sin πt 24 (t = time in weeks with t = 1 referring to the first week in the year). During which week(s) will the sales equal 98,490 items?

31 ft

To measure the width of a river, a surveyor starts at point A on one bank and walks 74 feet down the river to point B. He then measures the angle ABC to be 22°33'11''. Estimate the width of the river to the nearest foot. See the figure below.

90 yd

Two points A and B are on opposite sides of a building. A surveyor chooses a third point C 64 yd from B and 93 yd from A, with angle ACB measuring 67.3°. How far apart are A and B (to the nearest yard)?

√3/2

Use a sum or difference value to find the exact value sin 215° cos 95° - cos 215° sin 95°

-√6-√2/4

Use a sum or difference value to find the exact value sin 255°

π/3 , 2π/3

[0,2pi) ; sin s = sqrt3/3

cos^2 x

___ + sin^2 x = 1

csc x

___= 1 / sin x

5π/6

arccos(cos 7π/6)

√6-√2/4

cos (-75°)

-√3/3

cot 120°

-2

csc 330°

1

csc 450degrees

{60°, 120°, 240°, 300°}

interval [0,360] 4sin^2θ = 3

0, π, π/6, 5π/6

over the interval [0, 2π] 2sin^2x = sin x

π

over the interval [0, 2π] cos^2x + 2c OS X + 1 = 0

sin θ tan θ

sec θ - 1 /sec θ

0.8944

sin (arctan 2)

0.249328

sin 14°/ cos 14°

tan x

sin x = (___)(cos x)

2√5/5

sin(arctan 2)

und

tan (arcsin 2)

25

x1 = -4, x2= -3, x3 = -1, x4 = -2, and x5 = 0

{(4, 3), (-3, -4)}

x^2 + y^2 = 25 x - y = 1

{(9, 3), (-9, 3), (9, -3), (-9, -3)}

x^2 + y^2 = 90 x^2-y^2=72

π/4

y = cos^-1(√2/2)

determine the equation of the graph

y = sec 4x

π/3

y = sin^-1(√3/2)

π/4

y = tan-1 (1)

-30 degrees

θ = arcsin(-1/2)

30 degrees

θ = arctan(√3/3)

27deg

θ = cos-1(0.8910)

-29deg

θ = sin^-1(-0.4848)

66deg

θ = tan^-1(2.2460)