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mathematics
algebra and trigonometry graphs
Questions and Answers of
Algebra And Trigonometry Graphs
Convert to radian measure.-225°
An airplane has an airspeed of 150 km/h. It is to make a flight in a direction of 70° while there is a 25-km/h wind from 340°. What will the airplane’s actual heading be?
A 2500-kg block is suspended by two ropes, as shown. Find the tension in each rope. 45° 2500 kg 60°
Find the function value using coordinates of points on the unit circle. COS 4
Find the function value using coordinates of points on the unit circle. TT COS 6
Two cables support a 1000-lb weight, as shown. Find the tension in each cable. 60° 1000 lb 30°
Find the function value using coordinates of points on the unit circle. sin 5 п 6
A 150-lb sign is hanging from the end of a hinged boom, supported by a cable inclined 42° with the horizontal. Find the tension in the cable and the compression in the boom. 42° 150 lb
An airplane flies 032° for 210 mi, and then 280° for 170 mi. How far is the airplane, then, from the starting point, and in what direction is the plane moving?
Find polar notation for (cos θ + i sin θ)-1.
Find vector v from point A to the origin, where AB⇀= 4i - 2j and B is the point ( -2, 5).
Solve.2x - 4 = x + 8
Convert to a rectangular equation: = sec ||
Solve.4 - 5y = 3
Graph.y = 2x - 5
Graph.4x - y = 6
Graph.x = -3
Graph.y = 0
The center of a regular hexagon is at the origin, and one vertex is the point (4, 0°). Find the coordinates of the other vertices.
Find standard notation, a + bi.3(cos 30° + i sin 30°)
Find trigonometric notation. 1 - V3i
Find trigonometric notation. V2 2 + 9, 2 i
Find trigonometric notation.5i
Find a unit vector in the same direction as -4i + 3j .
Find trigonometric notation.√3 + i
For u = 2i - 7j and v = 5i + j, find 2u - 3v.
Two forces of 255 N and 325 N act on an object. The angle between the forces is 64°. Find the magnitude of the resultant and the angle that it makes with the smaller force.
Graph: r = 1 - cos θ.
Graph the complex number and find its absolute value.1 - 5i
Two forces of 410 N and 600 N act on an object. The angle between the forces is 47°. Find the magnitude of the resultant and the angle that it makes with the larger force.
Find trigonometric notation.-3i
Convert to a polar equation: x2 + y2 = 10.
Find trigonometric notation for 3 - 3i.
Solve the triangle, if possible. 23° 10 а 131° A C B
Find the absolute value of 2 - 3i.
Solve the triangle, if possible. 23° 10 а 131° A C B
Solve the triangle, if possible. B 38° a 24 21° C
Solve the triangle, if possible. B 38° a 24 21° C
Solve the triangle, if possible. C45.6° a B 42.1 34.2 A
Solve the triangle, if possible. A 34 36.5° C C 24 B
Graph the complex number and find its absolute value.4 + 3i
Express the indicated number in both standard notation and trigonometric notation. Imaginary axis -4 -2 + 2 -4 2 4 ● Real axis
Graph the complex number and find its absolute value.i
Find the area of ΔABC if C = 106.4°, a = 7 cm, and b = 13 cm.
Graph the complex number and find its absolute value.4 - i
Divide and express the result in standard notation a + bi: cos 2π | درا TT 8 cos 6 + i sin + i sin 2TT 3 bl 6
Points A and B are on opposite sides of a lake. Point C is 52 m from A. The measure of ∠BAC is determined to be 108°, and the measure of ∠ACB is determined to be 44°. What is the distance from
Express the indicated number in both standard notation and trigonometric notation. Imaginary. axis -4 -2 4 2 -4 2 4 Real axis
Two airplanes leave an airport at the same time. The first flies 210 km/h in a direction of 290°. The second flies 180 km/h in a direction of 185°. After 3 hr, how far apart are the planes?
Graph the complex number and find its absolute value.3
Graph: -4 + i.
Find polar coordinates of points A, B, C, and D. Give three answers for each point. 150° 180° 210⁰ 120° Co D 240° 90° 270° 60° A 30° 0 2 4 360° B 300⁰ 330°
Find the area of the triangle with C = 54°, a = 38 in., and b = 29 in.
Find (1 - i)8 and write standard notation for the answer.
Graph the complex number and find its absolute value.-5 + 3i
Convertto rectangular coordinates. -1, 2п 3
Find the polar coordinates of ( -1, √3). Express the angle in degrees using the smallest possible positive angle.
Find trigonometric notation.1 - i
Two forces of 32 N (newtons) and 45 N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the smaller force.
Find polar coordinates of points A, B, C, and D. Give three answers for each point. 5 п П 7 п В Зп он 2 4 2π D
Graph the complex number and find its absolute value.-i
Two forces of 50 N and 60 N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force.
Find standard notation. 2 (0 COS 7T 4 + i sin 7 TT 4
Graph the complex number and find its absolute value.4
Find standard notation. 12(cos 30° + i sin 30°)
Find trigonometric notation.2/5
Find standard notation. √5 (cos 0° + i sin 0°)
Find trigonometric notation.-2 - 2i
A parallelogram has sides of length 15.4 and 9.8. Its area is 72.9. Find the measures of the angles.
Find trigonometric notation.-3√2 - 3√2i
What restrictions must be placed on the variable in each of the following identities? Why?a) b) sin 2x = 2 tan x 1 + tan²x
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.7 cos 5θ cos 7θ
In Exercises, assume that all radicands are nonnegative.Rationalize the numerator: COS X tan x
Derive the identity. Check using a graphing calculator. tan x x (₁ TT + 4 = 1 + tan x 1 tan x
Solve, finding all solutions. Express the solutions in both radians and degrees. cos COS X = √3 2
Solve, finding all solutions. Express the solutions in both radians and degrees. sin x √2 2
Multiply and simplify. Check your result using a graphing calculator.(sin x - cos x)(sin x + cos x)
Solve, finding all solutions. Express the solutions in both radians and degrees. tan x -√3
Given that sin (3π/10) ≈ 0.8090 and cos (3π/10) ≈ 0.5878, find each of the following.a) The other four function values for 3π/10b) The six function values for π/5
Solve, finding all solutions. Express the solutions in both radians and degrees. COS X = 1 1 2
Multiply and simplify. Check your result using a graphing calculator.tan x (cos x - csc x)
Solve, finding all solutions. Express the solutions in both radians and degrees. sin x 2
Find an equivalent expression for each of the following. sec x + 2
Multiply and simplify. Check your result using a graphing calculator.cos y sin y (sec y + csc y)
Multiply and simplify. Check your result using a graphing calculator.(sin x + cos x)(sec x + csc x)
Find an equivalent expression for each of the following. cot x 2
Multiply and simplify. Check your result using a graphing calculator.(sin ϕ - cos ϕ)2
Solve, finding all solutions. Express the solutions in both radians and degrees. COS X V₂ 2
Find an equivalent expression for each of the following. tan x EN 2
Solve, finding all solutions. Express the solutions in both radians and degrees.tan x = -1
Solve, finding all solutions. Express the solutions in both radians and degrees. sin x √3 2
Multiply and simplify. Check your result using a graphing calculator.(1 + tan x)2
Find an equivalent expression for each of the following. csc x + (x TT 2
Multiply and simplify. Check your result using a graphing calculator.(sin x + csc x)(sin2 x + csc2 x - 1)
Multiply and simplify. Check your result using a graphing calculator.(1 - sin t)(1 + sin t)
Simplify and check using a graphing calculator 2 sin²x cos³x COS X 2 sin x 2
Simplify and check using a graphing calculator sec¹x tan+x sec²x 2 + tan²x
Factor and simplify, if possible. Check your result using a graphing calculator.sin x cos x + cos2 x
Factor and simplify, if possible. Check your result using a graphing calculator.tan2 θ - cot2 θ
Prove each of the following identities. (csc ß + cot B)² 1 + cos B 1 - cos B
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