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Use the Binomial Theorem to expand and simplify the expression. (x^2 + y^2 )^4
. x^8 + 4x^6 y^2 + 6x^4 y^4 + 4x^2 y^6 + y^8. Give all exact solutions over the interval [0°, 360°].
2 −sin 2 θ= 4 sin 2 θ
c. 30° + 360°n, 90° + 360°n, 150° + 360°n, 210° + 360°n, 270° + 360°n, 330° + 360°n, where n is any integer. Convert the rectangular equation to polar form. Assume a > 0. y^2 - 8x - 16 = 0 Convert the polar equation to rectangular form.
Use the Binomial Theorem to expand and simplify the expression. 2(x - 3)^4 + 5(x - 3)^2 c. 2x^4 - 24x^3 + 113x^2 - 246x + 207 Find the sum. Expand the binomial by using Pascal's Triangle to determine the coefficients. (2t - s)^5 c. 32t^5 - 80t^4 s + 80t^3 s^2 - 40t^2 s^3 + 10ts^4 - s^5 Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate.
4 cos 2 x− 1 = 0
Find the exact value of each expression. a. cos (120° + 45°) b. cos120° + cos45° Find the exact value of the cosine of the angle by using a sum or difference formula. 195° = 225° - 30° Convert the rectangular equation to polar form. Assume a > 0. x^2 + y^2 - 2ax = 0
. r= 2 acosθ
Use the Binomial Theorem to expand and simplify the expression. (2x + y)^3 d. 8x^3 + 12x^2 y + 6xy^2 + y^3 Find a polar equation of the conic with its focus at the pole. Conic: Parabola, Vertex or vertices: (1, -π/2) Plot the point given in polar coordinates and find two additional polar representations of the point, using -2π < θ < 2π.
Solve the equation for exact solutions over the interval [0, 2π].
sinx 2 = 2 –√−sinx 2
Convert the polar equation to rectangular form. Find a polar equation of the conic with its focus at the pole. Conic: Hyperbola, Eccentricity: e = 2, Directrix: x = 1 Convert the polar equation to rectangular form.
r= 2 sin 3 θ
d. (x^2 + y^2 )^2 = 6x^2 y – 2y^3 Solve the equation for exact solutions over the interval [0, 2π].
Give all exact solutions over the interval [0^0 , 360^0 ].
sinθ−sin 2 θ= 0
0° + 360°n, 60° + 360°n, 180° + 360°, 300° + 360°n, where n is any integer. Find the exact value of the trigonometric function given that and cos. (Both are in Quadrant II.) Note that answers in fractions must be entered like so: 4/5, 1/2, 3/4, -(5/10) sec ( v - u ) -(63/65) Solve each equation for exact solutions over the interval [0, 2π]. Write the expression as the sine, cosine, or tangent of an angle. Solve each equation for exact solutions over the interval [0, 2π].
-(44/117) Solve the equation for exact solutions over the interval [0, 2π].
cot 3 x= 3 –√
Solve each equation for exact solutions over the interval [0, 2π]. Find a formula for the sum of the first n terms of the sequence. Find a formula for the sum of the first terms of the sequence. 1, 5, 9, 13
Calculate the binomial coefficient. (^85 ) 56 Calculate the binomial coefficient. (^10098 ) 4950 Use the Binomial Theorem to expand and simplify the expression. Determine two coterminal angles (one positive and one negative) for each angle. Plot the point given in polar coordinates and find two additional polar representations of the point, using -2π < θ < 2π.
Determine two coterminal angles (one positive and one negative) for each angle. Give your answer in degrees using the following format: ex. 34, - 405,- Evaluate the sine, cosine and tangent of the real number. Write "undefined" if it's not possible. Find the period and amplitude. Select one: a. Period: 4π, Amplitude: 5/ b. Period: 5π, Amplitude: 1/ c. Period: 2π, Amplitude: 3 d. Period: π, Amplitude: 3
State the quadrant in which θ lies: Sin θ > 0 and tan θ < 0 Quadrant II Use the value of the trigonometric function to evaluate the indicated functions. sin t = 1/ i. csc(-t)
Determine two coterminal angles (one positive and one negative) for each angle. Give your answer in degrees using the following format: ex. 34, - 324,- Find the period and amplitude. Select one: a. Period: π/5, Amplitude: 3 b. Period: 3π, Amplitude: 1/ c. Period: 1, Amplitude: 1/ d. Period: 2π, Amplitude: 3 Find the period and amplitude. a. Period: π/5, Amplitude: 3 b. Period: 1, Amplitude: 1/ c. Period: 3π, Amplitude: 1/ d. Period: 2π, Amplitude: 3 Find a and d for the function f(x) = a cos x + d such that the graph of f matches the figure.
Determine two coterminal angles (one positive and one negative) for each angle. Determine the quadrant in which each angle lies. The answer should be in the following format: ex. Quadrant I a. 130° Quadrant II Use the Binomial Theorem to expand and simplify the expression. (a + 6)^4 Select one: a. a^4 + 24a^3 + 36a^2 + 212a + 1290
b. a^4 + 24a^3 + 216a^2 + 864a + 1296 c. a^4 + 12a^3 + 16a^2 + 64a + 12 d. a^4 + 4a^3 + 36a^2 + 144a + 21 Calculate the binomial coefficient.
20 C 15 15,
Find the sum using the formulas for the sums of powers of integers. Find the length of the arc on a circle of radius intercepted by a central angle θ. Radius: 15 inches Central Angle: 180^0 47.12 inches Use the given value to evaluate (if possible) all six trigonometric functions. If it isn't possible, answer with "undefined." Find the length of the arc on a circle of radius intercepted by a central angle θ. Radius: 3 meters Central Angle: 1 radian 300 Solve each equation for exact solutions over the interval [0, 2π].
Give all exact solutions over the interval [0°, 360°]. Solve each equation for exact solutions over the interval [0^0 , 360^0 ].
Convert the rectangular equation to polar form. Assume a > 0. y = 4 Select one: a. R = 3 sec θ b. R = 4 csc θ c. R = 4 d. R = 6 Find a polar equation of the conic with its focus at the pole. Conic: Parabola, Vertex or vertices: (5, π)
Choose an expression for the apparent nth term of the sequence. Assume that n begins with 1. 1, -1, 1, -1,1,... an = (-1)n + 1 Convert the polar equation to rectangular form.
r=4cscθr=4cscθ
Select one: a. (x^2 + y^2 )^2 = 6x^2 y – 2y^3 b. y = 4 c. X^2 + 4y – 4 = 0 d. X^2 + y^2 – x2/3^ = 0 e. 4x^2 – 5y^2 – 36y – 36 = 0 Find the exact value of the tangent of the angle by using a sum or difference formula. -165°
Expand the binomial by using Pascal's Triangle to determine the coefficients. (x - 2y)^5 c. x^5 + 10x^4 y + 40x^3 y^2 + 80x^2 y^3 + 80xy^4 + 32y^5 Convert the rectangular equation to polar form. Assume a > 0. 3x - y + 2 = 0 Solve each equation for exact solutions over the interval [0^0 , 360^0 ].
2 sinθ−1=cscθ
a. {90^0 , 210^0 , 330^0 } Convert the polar equation to rectangular form.
