Pre-calc

Use matrices to find the solution to the system of equations: -x-y=3 4x+5y=-14

(-1, -2)

Use matrices to find the solution to the system of equations: -3x+4y=-10 4x+2y-3z=-22 -4x-2y+z=18

(-2,-4,2)

Use matrices to find the solution to the system of equations: −2y+5z=0 −x−y−z=−4 −3x+y−5z=4

(-3, 5, 2)

Use addition or subtraction: sin(19π/12)

(-sqrt(2)-sqrt(6))/4

Use addition or subtraction: cos(165)

(-sqrt(6)-sqrt(2))/4

Use matrices to find the solution to the system of equations: 3x+2y=6 5x+4y=10

(2,0)

Use addition or subtraction: cos(75)

(sqrt(6)-sqrt(2))/4

Use addition or subtraction: sin(11π/12)

(sqrt(6)-sqrt(2))/4

Use half angles to find the exact value: cos(11π/12)

- sqrt(2+sqrt(3))/2

Given the equation (1/2) cos(3x + 2π) - 2, determine the period shift

-2π/3

Given tan A = -4/3, and sin A > 0, find Cos A

-3/5

Find the determinant of the matrix below -4 0 2 1

-4

Convert -π​/4 radians to degrees

-45

Find the determinant of the matrix below 5 -2 5 -3

-5

Given sin A < 5/13, and cos A < 0, find tan A

-5/12

Determine the Inverse of this matrix: 0 5 -2 -12

-6/5 -1/2 1/5 0

If cosx = 3/5, and x is in QIV, Find cos(2x)

-7/25

Use half angles to find the exact value: cos(5π/8)

-sqrt(2 - sqrt(2))/2

arctan(-sqrt(3))

-π/3

sin-1(-sqrt(3)/2)

-π/3

sin-1(-1/2)

-π/6

Use half angle formulas to find all solutions between [0,2π): 2sin(x/2) = sinx

0

arccos(1)

0

tan-1(0)

0

What are the dimensions of the matrix below? 4 ​1 ​−3 ​2 ​0

1 x 5

The current I, in amperes, flowing through a particular alternating current circuit at time, t seconds is: I = 240sin(30πt). What is the period

1/15

Given the equation (1/2) cos(3x + 2π) - 2, determine the amplitude

1/2

Given the equation f(t) = (1/2) cos(3t), determine the amplitude

1/2

Let point C be on circle A with radius 4 cm. BA is a radius. If angle ∠BAC is 3 radians. How long is arc BC?

12 cm

At the state fair, the giant Ferris wheel takes 48 seconds to make one full rotation. The Ferris wheel has a diameter of 60 ft. and the bottom of the wheel is 8 ft. above the ground. If you are the last person on the Ferris wheel and you board at the bottom, in the first 96 seconds when are you exactly halfway to the top? How high are you at that point?

12 sec, 36 sec, 60 sec, and 84 sec; 38 ft.

If tanx = 8/15, and x is located in Q3, Find cos(2x)

161/289

The vertices of the parallelogram below are given. Use matrices to find the area. A (0, 0) B (-1, 7) C(-3, 2) and D(-4, 9)

19

If a projectile is fired with velocity, v = 500 ft/s, at an angle x, then its range (the horizontal distance traveled) in feet, is modeled by the function: y = 250000sin(2x)/32 What angle should be used to reach an object 5000 feet away?

19.9 or 70.1 degrees

Given the equation y = -2sin(x - π) + 1, determine the amplitude

2

What size is the matrix below? -2 0 5 4 1 3

2 x 3

A park ranger at point A observes a fire and estimates the angle of elevation to be 25 degrees. Another ranger at point B, 5 miles due east of point A, estimates the angle of elevation to be 56 degrees. Determine the distance from point B to the fire.

2.14 miles

The vertices of the parallelogram below are given. Use matrices to find the area. A (0, 0) B (3, -1) C(5, 6) and D(8, 5)

23

At the state fair, the giant Ferris wheel takes 48 seconds to make one full rotation. The Ferris wheel has a diameter of 60 ft. and the bottom of the wheel is 8 ft. above the ground. If you are the last person on the Ferris wheel and you board at the bottom, in the first 96 seconds when are you at the top of the wheel? How high are you at the top of the wheel?

24 sec and 72 sec; 68 ft.

The current I, in amperes, flowing through a particular alternating current circuit at time, t seconds is: I = 240sin(30πt). What is the amplitude

240

If tanx = 8/15, and x is located in Q3, Find tan(2x)

240/161

If tanx = 8/15, and x is located in Q3, Find sin(2x)

240/289

The function y = -30cos(6t) + 37 models the height (in feet) of a specific seat on a Ferris wheel above the ground at time, t (in seconds). In the first 60 seconds, when is the seat at least 65 feet in the air?

26.49 seconds and 33.51 seconds

Given the equation f(t)=3\sin(t), determine the period.

2π

Given the equation, y = -2cosx, determine the period

2π

Given the equation (1/2) cos(3x + 2π) - 2, determine the period

2π/3

Given the equation f(t) = (1/2) cos(3t), determine the period

2π/3

cos-1(-1/2)

2π/3

The voltage E in an electrical circuit is modeled by E = 3.8cos(110πt). What is the maximum volatage

3.8

Convert 5π/3 ​radians to degrees.

300

In ABC, c = 15, b = 4.6, and Angle A = 106. Find the area.

33.2

What positive angle is co-terminal to 35

395

arccos(-sqrt(2)/2)

3π/4

Given the equation f(t) = -4sin(t/2), determine the period

4π

Convert 225 to radians

5π/4​

arccos(sin(4π/3))

5π/6

Find the determinant of the matrix below -5 -1 -4 -2

6

The vertices of the parallelogram below are given. Use matrices to find the area. A (0, 0) B (2, -7) C(8, 4) and D(10, -3)

64

In Triangle STR, t = 15, r = 16, angle S = 35. Find the area.

68.8

If sinx = 7/12, and x is located in Q1, Find tan(2x)

7sqrt(95)/23

If sinx = 7/12, and x is located in Q1, Find sin(2x)

7sqrt(95)/72

What entry is 5 in the matrix below? -2 0 5 4 1 3

A13

Solve the triangle: a = 26, c = 25, Angle B = 127

Angle A = 27.1, Angle C = 24.9, b = 45.6

Solve the triangle: a = 23, b = 29, Angle B = 102

Angle A = 33.7, Angle C = 44.3, b = 40.6

Solve the triangle: Angle C = 40, b = 35, c = 34

Angle A = 98.6, Angle B = 41.4, a = 52.3 OR Angle A = 1.4, Angle B = 138.6, a = 1.3

Solve the triangle: angle A = 37, a = 28, c = 26

Angle B = 109, Angle C = 34, and b = 44.

Solve the triangle: Angle A = 46, c = 9, a = 8.

Angle B = 80, Angle C = 54, b = 11 OR Angle B = 8, Angle C = 126, b = 1.5

The domain for y = sin-1x is all real numbers. T or F

False

The function y=tan(x) has an amplitude of 1. T or F

False

The translation matrix below represents a translation of 5 units right and 2 units down. T or F -5 -5 -5 2 2 2

False

cos(11π/6) = ​-sqrt(3)/2. T or F

False

cot = sin/cos. T or F

False

sin(3π/2)​ = 1. T or F

False

tanθ=5.831 has no solutions. T or F

False

the range of y = cosx is all real numbers. T or F

False

y = cosx has a domain of [-1,1]. T or F

False

y = sinx is an even function. T or F

False

What quadrant is the terminal side of theta = -320 in

I

Determine the Inverse of this matrix: -7 -5 7 5

Matrix is singular

Given Angle B = 139, a = 33, b = 15, how many triangles are possible

No triangles

Solve the triangle: Angle B = 108, a = 21, b = 19

Not a triangle

Solve the triangle: Angle C = 83, b = 29, c = 23

Not a triangle

Given that Angle B = 90, a = 17, and b = 27, how many triangles exist

One Triangle

If Matrix A is 4 x 3 and Matrix B is 3 x 2, then Matrix BA is undefined. T or F

True

Sec = 1/cos

True

The domain for y = sinx is all real numbers. T or F

True

The domain of y = tan-1x is all real numbers. T or F

True

The domain of y = tanx is all real numbers except π/2 + πn. T or F

True

The function y=tan(x) has an period of π. T or F

True

The range of y = tanx is all real numbers. T or F

True

The terminal side of (-3π​/4) is in Quadrant III. T or F

True

cos(π) = -1. T or F​

True

cotx = 1/tanx. T or F

True

f(x) = sin(x) has a domain of all real numbers. T or F

True

if theta = 215, the reference angle theta = 35. T or F

True

secx -tanxsinx = cosx. T or F

True

sin14cos11-cos14sin11 = sin3

True

y = cos(x) has a range of [-1,1]. T or F

True

y = cos(x) is an even function. T or F

True

Given Angle B = 64, a = 35, b = 33, how many triangles are possible

Two Triangles

Add or subtract unless undefined [−1​ 4​]+[−4 ​−6​]

[-5 -2]

Complete the identity = sin/cos + cos/sin

csc*sec

Use half angles to find the exact value: sin(67.5)

sqrt(2+sqrt(2))/2

Use half angles to find the exact value: sin(11π/12)

sqrt(2-sqrt(3))/2

(tan48 + tan12)/(1-tan48tan21)

sqrt(3)

cos(5π/12)cos(π/4) + sin(5π/12)sin(π/4)

sqrt(3)/2

Given tan A = sqrt(5), and cos A > 0, find sin A

sqrt(30)/6

Given cos A = -4/7, and tan A > 0, find Tan A

sqrt(33)/4

Reference Angle

the angle made with the terminal arm of the standard angle and the x-axis

Give all the angles between -2π < x< 2π that satisfy the equation: cosx = sqrt(3)/2

x = -11π/6, -π/6, π/6, 11π/g

Give all the angles between 0 < x< 360 that satisfy the equation: tanx = -2.167

x = 114.77 or 294.77

Give all the angles between 0 < x< 360 that satisfy the equation: cosx = -0.815

x = 144.59 or 215.41

Find all angles that satisfy the equation: sinx = -1

x = 3π/2 + 2πn

Give all the angles between 0 < x< 360 that satisfy the equation: tanx = 1.215

x = 50.54, 230.54

Give all the angles between 0 < x< 360 that satisfy the equation: cosx = 0.423

x = 64.98 or 295.02

Use factoring to find all solutions between [0,2π). 4cotx = cotxsin2x

x = π/2, 3π/2

Find all angles that satisfy the equation: sinx = sqrt(3)/2

x = π/3 + 2πn, 2π/3 + 2πn

Give all the angles between 0 < x< 4π that satisfy the equation: sinx = sqrt(2)/2

x = π/4, 3π/4, 9π/4, 11π/4

Find all angles that satisfy the equation: tanx = sqrt(3)/3

x = π/6 + πn

Find all solutions between [0,2π) cos(2x) - sinx = 0

x = π/6, 5π/6, 3π/2

Find all solutions between [0,2π) sin(2x) = cosx

x = π/6, π/2, 5π/6, 3π/2

Give all the angles between 0 < x< 4π that satisfy the equation: cosx = -1

x= π, 3π

In Pleasantown, GA, the average high tempertaure in January is 36 deg. F and the average high temperature in July is 80 deg. F. Which equation below models the temperature in Pleasantown in months after January?

y = -22cos(πx/6) + 58

At the state fair, the giant Ferris wheel takes 48 seconds to make one full rotation. The Ferris wheel has a diameter of 60 ft. and the bottom of the wheel is 8 ft. above the ground. If you are the last person on the Ferris wheel and you board at the bottom, which equation below models your height above the ground as a function of time?

y = -30cos(πx/24) + 38

At the harbor, the tide goes in and out. Low tide occurs at 4am and high tide occurs at 12pm. The difference between high and low tide is 15 feet. Which function below models height of the tide after 12am.

y = -7.5sin(πx/8) + 7.5

Given the equation y = -2sin(x - π) + 1, determine the equation for the midline

y = 1

Write the equation of the cosine function with an amplitude of 3, period of 4π, no phase shift, and a midline of -1.

y = 3cos(π/2) - 1

Write the equation of the sine function with an amplitude of 3, period of π, phase shift of π/2, and a midline of -2.

y = 3sin(2x - π) - 2

y = tan(x - π) + 1, determine the period

π

Which of the following does NOT represent a vertical asymptote for y=tan(x).

π + nπ

Determine the period: y = -3tan(2x)

π/2

cos-1(0)

π/2

cos-1(cos(3π/2))

π/2

arcsin(sqrt(2)/2)

π/4

If theta = 5π​/4, what is the reference angle theta

π/4​