Chapter 4.5-4.8

cos (arccot u)

(u(√u^2 + 1))/ u^2 + 1

Use a tangent function to estimate the grade resistance of a 2500-lb car travelling on a -2.9° grade.

-127 pounds

cot x = 2 sec x

0.427, 2.715

cos(to the power of -1) (cos x) = 2.2

2.2

cos(to the power of -1) (-0.7221)

2.378

From a boat on the river below a dam, the angle of elevation to the top of the dam is 18°48'. If the dam is 734 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

2156 ft

Determine whether the function is periodic. If it is periodic, find the period. f(x) = 7 sin 2x + 2 cos 3x

2π

arcsin 0.72

46.05°

The equation θ = cos^-1 (R/Z) gives the phase angle between R and Z in an AC circuit. Find θ if R = 40 ohms and Z = 60 ohms.

48.2°

cosθ = 0.5576, 0° ≤ θ≤ 90°

56.11°

sec x = √2, 3π /2≤x≤ 2π

5π /4

Tell whether the function exhibits damped oscillation. If it does, identify the damping factor and tell whether the damping occurs as x approaches ∞ or as x approaches 0. f(x) = 5x sin 2x

Damping factor = 5x Damping occurs as x approaches 0

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x) = cos(to the power of -1) (2x)

Domain: (-π/6, π/6) Range: (5π/6, π/6) decreasing origin symmetry upper and lower bounded

Find the domain and range of the function. f(x) = 4 sin l x l

Domain: (-∞ , ∞ ) Range: [-4, 4]

Determine whether the graph of f(x) is a sinusoid. f(x) = sin 15x + cos 13x

No

City X is 55 miles due south of City Y, and City Z is 40 miles due west of City X. What is the bearing of City Z from City Y (to the nearest tenth of a degree)?

S 36°W

Analyze the function for domain, range, continuity, symmetry, boundedness, extreme, asymptotes, and end behavior. f(x) = - tan x

domain: x ≠ (π/2)n range: (-∞,∞) symmetry: yes, along origin unbounded no local extrema asymptotes: all integers of (π/2) continuous

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. f(x) = arcsin (x/5)

horizontal stretch by a factor of 5

Find a ,b, and h so that f(x) = a sin (b(x-h)). f(x) = 2 sin πx + 3 cos πx

a = 3.61 b = 3.41 h = -0.31

Describe the end behavior of the function. f(x) = e(to the power of -x) cos 3x

lim f(x) = 0 (as x approaches infinity)

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. y = -cot x

reflection across the x axis

Find the angle θ (if it exists) in the interval [0°, 90°) for which sin θ = cos θ.

θ = 45°

y = cos(to the power of -1) (√3/2)

π/6

cos (arcsin(1/4))

√15/4