Assume that sin(.42) = .41. Use properties of the cosine and sine to determine sin(-.42), sin(6p - .42), and cos(.42).
> Find the following indefinite integrals. ∫2 sin x/2 dx
> Richard Stone (see Exercise 32) determined that the yearly consumption of food in the United States was given by f (m, p, r) = (2.186) m0.595 p-0.543 r0.922. Determine which partial derivatives are positive and which are negative, and give interpretati
> Find the following indefinite integrals. ∫-1/2 cos x/7 dx
> Find the following indefinite integrals. ∫3 sin 3x dx
> Find the following indefinite integrals. ∫cos 2x dx
> Find the equation of the line tangent to the graph of y = 3 sin 2x - cos 2x at x = 3 π/4.
> Find the equation of the line tangent to the graph of y = 3 sin x + cos 2x at x = π/2.
> Find the slope of the line tangent to the graph of y = sin 2x at x = 5 π/4.
> Find the slope of the line tangent to the graph of y = cos 3x at x = 13π/6.
> Differentiate (with respect to t or x): y = (cos t) ln t
> Differentiate (with respect to t or x): y = sin(ln t)
> Differentiate (with respect to t or x): y = ln(sin 2t)
> Using data collected from 1929 to 1941, Richard Stone determined that the yearly quantity Q of beer consumed in the United Kingdom was approximately given by the formula Q = f (m, p, r, s), where f (m, p, r, s) = (1.058) m0.136 p-0.727 r0.914 s0.816 a
> Differentiate (with respect to t or x): y = ln(cos t)
> Differentiate (with respect to t or x): y = cos (e2x+3)
> Differentiate (with respect to t or x): y = sin t / cos t
> Differentiate (with respect to t or x): y = (1 + x) /cos x
> Differentiate (with respect to t or x): y = sin 2x cos 3x
> Differentiate (with respect to t or x): y = (cos x + sin x)2
> Differentiate (with respect to t or x): y = ex sin x
> Differentiate (with respect to t or x): y = cos2 x + sin2 x
> Differentiate (with respect to t or x): y = cos2 x3
> Differentiate (with respect to t or x): y = 3√(sin π t)
> The volume (V) of a certain amount of a gas is determined by the temperature (T) and the pressure (P) by the formula V = .08(T/P). Calculate and interpret ∂V/∂P and ∂V/∂T when P = 20, T = 300.
> Differentiate (with respect to t or x): y = (1 + cos t)8
> Differentiate (with respect to t or x): y = ecos x
> Differentiate (with respect to t or x): y = √ sin(x - 1)
> Differentiate (with respect to t or x): y = cos(ex)
> Differentiate (with respect to t or x): y = sin √(x – 1)
> Differentiate (with respect to t or x): y = sin3 t2
> Differentiate (with respect to t or x): y = cos3 t
> Differentiate (with respect to t or x): y = cos (2x + 2) / 2
> Differentiate (with respect to t or x): y = sin (π - t)
> Differentiate (with respect to t or x): y = t cos t
> The demand for a certain gas-guzzling car is given by f (p1, p2), where p1 is the price of the car and p2 is the price of gasoline. Explain why ∂f/∂p1 < 0 and ∂f/∂p2 > 0.
> Let g (x, y, z) = x/(y - z). Compute g (2, 3, 4) and g (7, 46, 44).
> Differentiate (with respect to t or x): y = t cos t
> Differentiate (with respect to t or x): y = - sin 3t / 3
> Differentiate (with respect to t or x): y = 2 cos 3t
> Differentiate (with respect to t or x): y = cos (- 4t)
> Differentiate (with respect to t or x): y = 4 sin t
> Differentiate (with respect to t or x): y = 2 cos 2t
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 16 4 1
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 3 2
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. t √5 2
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 2 t √3 1
> Let p1 be the average price of MP3 players, p2 the average price of audio files, f (p1, p2) the demand for MP3 players, and g (p1, p2) the demand for audio files. Explain why ∂f/∂p2 < 0 and ∂g/∂p1 < 0.
> In any given locality, the length of daylight varies during the year. In Des Moines, Iowa, the number of minutes of daylight in a day t days after the beginning of a year is given approximately by the formula (Source: School Science and Mathematics.) (
> In any given locality, tap water temperature varies during the year. In Dallas, Texas, the tap water temperature (in degrees Fahrenheit) t days after the beginning of a year is given approximately by the formula (Source: Solar Energy.) (a) Graph the fu
> Assume that cos(.19) = .98. Use πroπerties of the cosine and sine to determine sin(.19), cos(.19 - 4π), cos(-.19), and sin(-.19).
> Determine the value of cos t when t = 5π, -2π, 17π>2, -13π>2.
> Determine the value of sin t when t = 5π, -2π, 17π>2, -13π>2.
> Use the unit circle to describe what happens to sin t as t increases from π to 2π.
> Refer to Fig. 10. Describe what happens to cos t as t increases from 0 to Ï€. Figure 10: (a) P T I (d) P Ø (b) P (e) P O
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -cos t
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = cos t
> Refer to Exercise 27. Let g (p1, p2) be the number of people who will take the train when p1 is the price of the bus ride and p2 is the price of the train ride. Would you expect ∂g/∂p1 to be positive or negative? How about ∂g/∂p2? Exercise 27: In a cert
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -sin(-π>3)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -sin(π>6)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -sin(3π>8)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = sin(-4π>3)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = sin(7π>6)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = sin(3π>4)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-3π/4)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-5π/8)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-4π/6)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(5π/4)
> In a certain suburban community, commuters have the choice of getting into the city by bus or train. The demand for these modes of transportation varies with their cost. Let f (p1, p2) be the number of people who will take the bus when p1 is the price of
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(3π/2)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-π>/6)
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = 1.1 and b = 3.5, find a and c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .5 and a = 2.4, find b and c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .9 and c = 20.0, find a and b. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .4 and a = 10.0, find c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .4 and c = 5.0, find a. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = 1.1 and b = 3.2, find c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = 1.1 and c = 10.0, find b. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. Estimate t if a = 12, b = 5, and c = 13. Figure 16: t a b
> Match the graph of the function to the systems of level curves shown in Figs. 8(a)–(d). Figure 8: 2 2= ex² + e-4y² 2 e (b) 2₂x0 몸 라 (d) 2.
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. t (.8, -.6)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (-.6, -.8)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (.6, .8)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (-2, 2)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (2, -3)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (-2, 1)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. t 3 5
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 13, t 12
> Convert the following to radian measure. 990˚ , - 270˚ , - 540˚
> Convert the following to radian measure. 450˚ , -210˚ , -90˚
> Match the graph of the function to the systems of level curves shown in Figs. 8(a)–(d). Figure 8: NY 2 15x²y²e-2². x² + y² 150 107 e (b) 2₂x0 몸 라 (d) 2.
> Convert the following to radian measure. 18 ˚, 72˚ , 150 ˚
> Convert the following to radian measure. 30 ˚, 120˚, 315˚
> Construct angles with the following radian measure. 2π/3, - π/6, 7π/2
> Construct angles with the following radian measure. π/6, - 2π/3, - π
> Construct angles with the following radian measure. - π/4, - 3π/2, - 3π
> Construct angles with the following radian measure. - π/3, - 3π/4, - 7π/2
> Construct angles with the following radian measure. π/3, 5π/2, 6π
> Construct angles with the following radian measure. 3π/2, 3π/4, 5π
> Give the radian measure of each angle described.
> Give the radian measure of each angle described. 0
