PRECAB Final

180°; 𝜋 radians

(-1, 0) is the coordinate of a point on the unit circle. If 𝛳 is the angle corresponding to this point, find the degree and radian measure of 𝛳.

hyperbola

4x^2 - 6y^2 + 2x - 7y - 2 = 0 represents a/an

3 cos 𝜋t/8

A buoy bobbing up and down in the water moves from its highest point to lowest point and then back to its highest point in 16 seconds. The distance between the highest and lowest points is 6 feet. Which of the following sinusoidal functions BEST describes this situation? (At t = 0, the function is at its highest point.)

42.2 N; 100.7°

A constant force of 18 newtons is being applied at a constant angle of 56° on an object at the same time that a constant force of 32 newtons at a constant angle of 124° is acting on the object. What is the magnitude and direction of the resultant force?

𝜋/70

A musical note creates a sound wave modeled by the equation y = 1.5 sin (140t) where t is the time in seconds. What is the period of this function?

⟨-206.087, 184.088⟩

A plane is flying at 250mph on a bearing of 150°. It is blown off course by a wind blowing at 60 mph on a bearing of 80°. What is the vector of the course the plane is actually flying?

138°

A plane is flying at an air speed of 450 mph in a trig direction of 140°. If the wind is blowing at 30 mph in the trig direction of 110°. To the nearest degree, what is the resultant direction of the plane?

(-2√2, -2√2)

A robotic vacuum is positioned so a point on it has polar coordinates (4, 5𝜋/4). Find rectangular coordinates for this point.

x^2 = 20y

A solar oven uses a parabolic reflector to focus the sun's rays at a point of 5 inches from the vertex of the reflector (see diagram). Write an equation for a cross section of the oven's reflector with its focus on the positive y-axis and its vertex at the origin.

25.2 ft

Aaron kicked a soccer ball with an initial velocity of 39 feet per second at an angle of 44° with the horizontal. After 0.9 seconds, how far has the ball traveled horizontally?

x^2/25 + y^2 = 1

All elliptical stained-glass insert is to be fitted in a 10 ft by 2 ft rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

613.4 mph

An airplane is flying due east with a velocity of 550 miles per hour. The wind blows at 80 miles per hour at an angle of 40° North of East. Determine the velocity of the airplane's flight.

11π/9

Change 220° to radians.

40°

Change the radian measure 2π/9 to degrees.

Center: (-2, -4); Radius: √13

Complete the square to write the standard form of the circle below and then find its center and radius. 2x^2 + 2y^2 + 8x + 16y + 14 =0

y = (2x - 5)/(x - 2)

Find a rectangular equation for the parametric equations: x = 2 + 1/t and y = 2 - t

⟨-√5/5, 2√5/5⟩

Find a unit vector with the same direction as v = ⟨-2, 4⟩.

{30°, 150°, 270°}

Find all solutions for 0° ≤ x < 360°. 2 cos^2 x = sin x + 1

0, 𝜋, 3𝜋/4, 7𝜋/4

Find all solutions of the equation on the interval [0, 2𝜋). sex^2 x + tan x = 1

2√2/3

Find cos 𝛳 if sin 𝛳 = -1/3 and 𝛳 is in the fourth quadrant.

480°, -240°

Find one positive and one negative angle that is coterminal with 120°.

(4, 2𝜋/3)

Find polar coordinates for the point with rectangular coordinates (-2, 2√3) if 0 ≤ 𝛳 ≤ 2𝜋 and r ≥ 0.

68.95 cm^2

Find the area of △ABC if ∠B = 52°, a = 12.5, and c = 14 cm.

⟨-15, 1⟩; 15.03

Find the component form and magnitude of (see image) with initial point A(9, 2) and terminal point B(-6, 3).

𝛳 = -𝜋/3

Find the equation represented in the given graph.

Focus: (4, 2); Directrix x = -2

Find the focus and directrix of the parabola: x = 1/12(y - 2)^2 + 1

8.9 cm

Find the length to the nearest hundredth of the shortest side of △CHS if ∠C = 40°, ∠H = 60°, and side h = 12 cm.

53°

Find the measure of ∠B to the nearest degree in the triangle if a = 12 and c = 20.

18.432

For a photography project, Maris is photographing deer from a tree stand. From her sight 30 feet above the ground, she spots two deer in a straight line as shown in the diagram below. How much farther away is the second deer than the first? Round your answer to the three decimal places.

1

For all values of 𝛳, sin^2 𝛳 + cos^2 𝛳 is equal to which of the following?

(8, 2), (-2, 2), (3, 3), (3, 1)

Given the ellipse represented by the equation (x - 3)^2 / 25 + (y - 2)^2 = 1, find the coordinates of the vertices and co-vertices.

10.8

Given the right triangle ABC with ∠B = 90°. Find the measure of side b to the nearest tenth if ∠A = 22° and c = 10.

y = tan x/4

Identify the function that is graphed.

-4/3

If csc 𝛳 = -5/4 on the interval (3𝜋/2, 2𝜋), find tan 𝛳.

𝜋/2, 3𝜋/2

If sin^2 x = 1 for 0 ≤ x ≤ 2𝜋, then x equals which of the following?

-1/2

If x = 𝜋/6, find sin(x + 𝜋).

17.61

If △ABC, ∠B = 52°, a = 9, and b = 14. Find c.

x = (120 cos 38°)t and y = (120 sin 38°)t - 16t^2

Jacob hit a golf ball with initial velocity of 120 feet per second at an angle of 38° with the ground. Write parametric equations to represent this situation.

4.16 miles

Jan and Sam are hiking on a trail that splits into two forks. They decide to split up and each explore a different fork. (The forks diverge at an angle of 67°.) If Sam walks at a speed of 3.5 mi/h and Jan walks at a speed of 4 mi/h, how far apart are the hikers after 1 hour?

u and v have the same magnitude and direction

Let P(0, 0) and Q(3, 2) be the initial and terminal points of vector u. Let R(1, 2) and S(4, 4) be the initial and terminal points of vector v. Which of the following is true?

⟨10, 12⟩

Let v = ⟨-4, 0⟩ and w = ⟨-2, 4⟩. Find 3w - 4v.

x-coordinate.

On a unit circle, the value for cos 𝛳 can be determined by looking at the

(0, -2 +/- √37)

Refer to the hyperbola represented by (y + 2)^2/36 - x^2 = 1. Find the coordinates of the foci.

y + 2 = +/-6x

Refer to the hyperbola represented by (y + 2)^2/36 - x^2 = 1. Write the equations of the asymptotes.

sin^2 x

Simplify sec^2 x - tan^2 x - cos^2 x.

-tan^2 x

Simplify sin^2 x - sec^2 x + cos^2 x.

2 cot^2 x

Simplify: cos x / (sec x - 1) + cos x / (sec x + 1)

𝜋/4 + 2n𝜋, 7𝜋/4 + 2n𝜋

Solve 4 sin^2 x + 4√2 cos x - 6 = 0 for all values of x.

𝜋

Solve cos 𝛳 = -1 for 0 ≤ 𝛳 ≤ 2𝜋.

80.4°, 279.6°, 120°, 240°

Solve for 0° ≤ x ≤ 360°. 12 sin^2 x - 4 cos x - 11 = 0

{2𝜋/3, 5𝜋/3}

Solve tan 𝛳 = -√3 for [0, 2𝜋).

9.7 ft

The angle of elevation of a 12 ft ladder leaning against a wall is 36°. How far is the base of the ladder from the wall?

15√3 m

The angle of elevation, 𝛳, from point A to the top of the tree is 60°. If point A is 15 m from the base of the tree, how tall is the tree?

13.332, 113.363°

The component form of a vector is ⟨-5.287, 12.239⟩. What is the magnitude and direction of the vector?

y = sin (x + 𝜋/4)

The equation of the function that will translate the sine function of 𝜋/4 to the left is which of the following?

y = 3/2 sin (2𝜋/3)x

The figure below shows the graph of one complete cycle of a sine function. Which of the following is an equation of this function?

cardioid.

The polar equation r = 2 + 2 sin 𝛳 can best be described as a/an

(-∞.∞)

The range of y = 4 tan x is which of the following?

117.2°

Two windmills stand on a field 456 feet apart. A cow is in the field, 320 feet from one windmill and 210 feet from the other. What is the measure of 𝛳?

-7/40

Two wires support a utility pole and form angles 𝛼 and 𝛽 with the ground. Find the value of tan (𝛼 - 𝛽) if tan 𝛼 = -3/5 on (𝜋/2, 𝜋) and tan 𝛽 = -5/13 on (𝜋/2, 𝜋).

(-√2 - √6)/4

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

1

What is the simplest form of 1/(sin^2 x) - (cos^2 x)/(sin^2 x)?

-√3

What is the value of cot (-𝜋/6)?

-.8329

What is the value of sin(236.4°)?

What is the value of the sec A to four decimal places if a = 10 and b = 5?

What is the value of the sec A to four decimal places if a = 10 and b = 5?

60°

Which angle is the reference angel for 240°?

tan 𝛳 = sin 𝛳 sec 𝛳

Which equation is a trig identity?

-cos 𝛳

Which expression is equivalent to cos (𝛳 - 𝜋)?

-𝜋/2 ≤ y ≤ 𝜋/2

Which interval below is the range of the inverse sine function, arcsin x?

y=-4 sin x/3

Which of the following trig functions has an amplitude of 4 and a period of 6𝜋?

y = cos x

Which trigonometric function is not an odd function?

x^2 + y^2 - 2y = 0

Write the polar equation r^2 - 2r sin 𝛳 = 0 in rectangular form.

√5/5

𝛳 is an angle in standard position which passes through (-2,1). Find sin 𝛳.