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mathematics
algebra and trigonometry graphs

Questions and Answers of Algebra And Trigonometry Graphs

Simplify.cos (u + v) cos v + sin (u + v) sin v
Simplify.sin (u - v) cos v + cos (u - v) sin v
Find an identity for cos (u + v) involving only cosines.
Solve.x - 7 = x + 3.4
Given that sin 31° = 0.5150 and cos 31° = 0.8572, find the specified function value.sec 59°
In a circus, a guy wire A is attached to the top of a 30-ft pole. Wire B is used for performers to walk up to the tight wire, 10 ft above the ground. Find the angle ϕ between the wires if they are
An art student’s eye is at a point A, looking at a mural of height h, with the bottom of the mural y feet above the eye. The eye is x feet from the wall. Write an expression for θ in terms of x,
Given that sin 31° = 0.5150 and cos 31° = 0.8572, find the specified function value.tan 59°
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show
For a rope course and climbing wall, a guy wire R is attached 47 ft high on a vertical pole. Another guy wire S is attached 40 ft above the ground on the same pole. Find the angle α between
Solve ecos x = 1 in [0, 2π).
Given that f(x) = cos x, show that f(x + h) − f(x) h = COS X cos h h 1 ¹) sin x sin h h
Given that f(x) = sin x, show that f(x + h) = f(x) h h- h = sin x (cos / -1) + cos x (sin) h h
Why are the ranges of the inverse trigonometric functions restricted?
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show
Miles lists his answer to a problem as π/6 + kπ, for any integer k, while Jaylen lists his answer as π/6 + 2kπ and 7π/6 + 2kπ, for any integer k. Are their answers equivalent? Why or why not?
What is the difference between a trigonometric equation that is an identity and a trigonometric equation that is not an identity? Give an example of each.
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show
Derive the identity. Check using a graphing calculator. п (x - 37 2 sin x = COS X
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show
Derive the identity. Check using a graphing calculator. sin (a +B) + sin (a - ß) = 2 sin a cos B
Find an identity for cos 2θ. 2θ = θ + θ.
Find an identity for sin 2θ. 2θ = θ + θ.
Derive the identity. Check using a graphing calculator. sin (a + B) cos (a - B) tan a + tan B 1 + tan a tan B
Determine the horizontal asymptote of the graph of the function. f(x) = x5 x³ + x X
Solve.2x3 + x2 < 10 + 11x
Solve.x3 + 5x2 - 25x ≤ 125
Simplify. i11
Simplify.i7
Simplify. i35
Simplify.i24
Simplify. i64
Simplify.i42
Simplify.( -i)71
Simplify. (5i)4
Simplify.(2i)5
Solve.2x2 > 5x + 3
Solve.x2 + x - 2 > 0
Solve.x2 - x - 6 > 0
Solve.x2 - x - 5 ≥ x - 2
Solve.x2 > 25
Graph the piecewise function. g(x) -x+ 3, for x = -2, 4, 2x 3 for 2 < x < 1, for x ≥ 1
Graph the piecewise function. -x², h(x)=x+1, for x < -2, for-2 ≤ x < 0, x³ - 1, for x ≥ 0
Solve.x2 + 4x + 7 ≥ 5x + 9
Solve.x2 ≤ 1
Solve.4 - x2 ≤ 0
Solve.11 - x2 ≥ 0
Solve.6x - 9 - x2 < 0
Solve.x2 + 2x + 1 ≤ 0
Solve.x2 + 12 > 4x
Solve.x2 - 8 > 6x
Solve.4x3 - 7x2 ≤ 15x
Solve.2x3 - x2 < 5x
Solve.x3 + 3x2 - x - 3 ≥ 0
Solve.x3 + x2 - 4x - 4 ≥ 0
Solve.x3 - 2x2 < 5x - 6
Solve.x3 + x ≤ 6 - 4x2
Solve.x5 + x2 ≤ 2x3 + 2
Solve.x5 + 24 > 3x3 + 8x2
Solve.2x3 + 6 ≤ 5x2 + x
Solve.x3 - 9x + 27 ≤ 3x2
Solve.0.1x3 - 0.6x2 - 0.1x + 2 < 0
Solve.19.2x3 + 12.8x2 + 144 ≥ 172.8x + 3.2x4
Solve. Find exact solutions.2x2 + 12 = 5x
Solve. Find exact solutions.7x2 + 4x = 3
The following table lists the newspaper revenue, in billions of dollars, from classified ads for selected years from 1975 to 2013.a) Use a graphing calculator to fit cubic and quartic functions to
For what values of k will the remainder be the same when x2 + kx + 4 is divided by x - 1 and by x + 1?
Find a 15th-degree polynomial for which x - 1 is a factor.
A dog’s life span is typically much shorter than that of a human. Age equivalents for dogs and humans are listed in the following table.a) Use a graphing calculator to fit linear and cubic
Find the nonlinear asymptote of the function. f(x) x² + 3x² 4 x² + 1 2
Graph the function. f(x) = = 2x³ + x² x³ 3 8x - 4 + x² - 9x - 9
Graph the function. f(x) = x³ + 4x² + x - 6 x²-x-2
Solve.2y - 3 ≥ 1 - y + 5
Solve.(x - 2)(x + 5) > x(x - 3)
Raleigh, North Carolina, is one of the fastest growing cities in the United States. In 2014, the population was approximately 438,000, and the growth rate was about 3.4% per year.a) Find the
Solve.| x + 6| ≥ 7
Find each of the following, to four decimal places, using a calculator.e4
Find each of the following, to four decimal places, using a calculator.e10
Find each of the following, to four decimal places, using a calculator. e 2
Find each of the following, to four decimal places, using a calculator.e-2.458
On November 20, 2014, Georgia O’Keeffe’s painting, “Jimson Weed/White Flower No. 1,” sold at Sotheby’s auction in New York City for $44.4 million, a record price for any female artist’s
Express as a product.logb t3
Find each of the following. Do not use a calculator.log2 16
Express as a product.loga x4
Find each of the following. Do not use a calculator.log3 9
Graph the function.f(x) = 4-x
Express as a product.log y8
Find each of the following. Do not use a calculator.log5 125
Graph the function.f(x) = log x
Express as a product.ln y5
Find each of the following. Do not use a calculator.log2 64
Graph the function.f(x) = ex - 3
Graph the function.f(x) = ln (x + 2)
Express as a product.logc K-6
Find each of the following. Do not use a calculator.log 0.001
Find each of the following. Do not use a calculator.log 0.00001
Express as a product.logb Q-8
Find each of the following. Do not use a calculator.log 100

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