Finding the Central Angle In Exercises 53 and 54,find the radian measure of the central angle of a circle ofradius r that intercepts an arc of length s.53. r = 80 kilometers, s = 150 kilometers54. r = 14 feet, s = 8 feet

Finding the Central Angle In Exercises 53 and 54,find the radian measure of the central angle of a circle ofradius r that intercepts an arc of length s.53. r = 80 kilometers, s = 150 kilometers54. r = 14 feet, s = 8 feet

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Trigonometry

Section1.1: Radian And Degree Measure

Problem 54E: Finding the Central Angle In Exercises 53 and 54, find the radian measure of the central angle of a...

See similar textbooks

Related questions

Q: Find the four fourth roots of z= cos 4p/3 i+ sin 4p/3 . Leave your answers in trigonomet-ric form.

A: De Moivre's law: cosθ+isinθn=cos nθ+isin nθ.

Q: Find (1 + i)10.

Q: Resultant Force Three forces with magnitudes of70 pounds, 40 pounds, and 60 pounds act on an objecta...

A: Given Three forces with magnitudes of 70 pounds, 40 pounds, and 60 pounds act on an object at angle...

Q: Graph one complete cycle of each of the following. In each case, label the axes accuratelyand identi...

A: Given the following function: y = 2 + sin x The objective is to graph one complete cycle of the abov...

Q: Find the measures of the numbered angles in the isosceles trapezoid. mZ1 = 690

A: Answer

Q: Think About It Consider the functionsf(x) = x + 2 and f −1(x) = x − 2. Evaluate f( f −1(x))and f −1(...

A: fx=x+2 & f-1x=x-2 Now when x=-10, ff-1-10=f-10-2=f-12=-12+2=-10 f-1f-10=f-1-10+2=f-1-8=-8-2=-1...

Q: Using Trig to Find the Missing Sides Find the value of 'x' rounded to the nearest hundredth.

A: Here we have to find the value of x=?

Q: Finding a Polynomial Function withGiven Zeros In Exercises 65–70, find thepolynomial function f with...

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want rem...

Q: Find all degree solutions for each of the following: cos 3u = 0

A: Given: cos3u=0 We know that value of cosθ is zero at odd multiple of 90∘

Q: Given that i is the base of the imaginary numbers, justify why i' must be equal to -i?

A: To Prove i3=-i

Q: (-28 + 7 + 71r-48-)-(7-6) A)ア-7r+4+ 7r-6 B) - ór+3+ 7r-6 2 -6r +5+ 7r-6 C) D)r-ór+2

A: We have to solve:

Q: Which of the following represents the solution set to the equation: x-16x + 65 = 0? (1) 8±2i (3) –16...

A: From the given data:

Q: Give the exact value of each of the following. sin pi/ 2

A: Given: y=sinπ2 For finding value of given expression, we draw graph of sine function as below

Q: Name the reference angle for each of the following angles. -140 degree

A: Name the reference angle for each of the following angles.

Q: An ________ solution is a solution that does not satisfy the original equation.

A: An ________ solution is a solution that does not satisfy the original equation

Q: Graph one complete cycle of each of the following. In each case, label the axes accurately. y = - ...

A: Given: y=-14 tan xThe one complete cycle is ...

Q: State the reference angle theorem.

A: Reference angle: The smallest angle that the terminal side of a given angle makes with the x axis. ...

Q: For each of the following equations, solve for (a) all radian solutions and (b) x if0 <= x < 2...

A: Given The equation is sin x = -0.8125 .

Q: 62 T in radians is 9 The angle between 0 and 27 in radians that is coterminal with the angle

Q: To prove, or verify, an identity, we can start with the _____ ______ of the equationand __________ i...

A: We know that to prove, or verify, an identity, we can start with the left hand side of the equation ...

Q: Writing an Equation In Exercises 75–78,write an equation for a function with thegiven characteristic...

A: You posted multiple questions, I'll answer the first question. For all the remaining questions to be...

Q: Writing a Complex Number in StandardForm In Exercises 11–22, write thecomplex number in standard for...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Solve each equation for exact solutions over the interval 30°, 360°2 where appropriate.Give approxim...

A: "Since you have asked multiple questions we will solve the first question for you. If you want any s...

Q: Prove that sin theta(csc theta + cot theta) = 1 + cos theta is an identity by transforming the left ...

A: Given : sin θ (csc θ + cot θ) = 1 + cos θ Taking LHS : = sin θ (csc θ + cot θ) = sin θ (1/sin θ + ...

Q: Solving a Polynomial Equation InExercises 85–90, solve the equation. Checkyour solutions.

A: Polynomial: 85. 6x4-54x2=0=>6x2(x2-9)=0=>6x2(x+3)(x-3)=0x=0,-3,386. 5x3+30x2+45x=...

Q: Sketch the graph of y = -3 tan 1/2 x. Which of the following matches your graph?

A: Given, y=-3tan12x

Q: a scientist is standing at the top of a mountain 2 mi above sea level measures the angle of depressi...

A: Here a scientist is standing at the top of a mountain 2 mi above sea level measures the angle of de...

Q: Find the following products. (2 + 6i)(2 - 6i)

A: Use the formula a+ba-b=a2-b2, to find the product. 2+6i2-6i=22-6i2=4-36i2

Q: What happens when you try to find A for sin A = 1.234 on your calculator? Why doesit happen?

A: What happens when you try to find A for sin A = 1.234 on your calculator? Why does it happen? Given ...

Q: 4.

Q: Multiple choice for 9 and 10.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question ...

Q: Using a Reference Angle In Exercises55–68, evaluate the sine, cosine, and tangentof the angle withou...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Sketch one complete cycle of each of the following by first graphing the appropriate sine orcosine c...

A: y=3cosec2x-π3 Now the graph of y=3sin2x-π3 is,

Q: If z1 =3 - 5i and z2 =26 -2i, find z1 +z2 and z1 -z2.

A: Given that, z1 = 3 - 5i z2 = 26 -2i We have to find z1 + z2 and z1 - z2.

Q: Determine whether the graph of the given equation will be a line, circle, rose curve, lemnis-cate, c...

A: Given The equation of the polar curve is r=4+4 cos θ .

Q: Angle of Elevation From a point on the ground, a person notices that a 110-footantenna on the top of...

A: Given Angle of Elevation From a point on the ground, a person notices that a 110-foot antenna on the...

Q: Arc Length A satellite 200 miles above the earth is orbiting the earth once every6 hours. How far do...

A: Here the central angle θ for 6 hours and radius of the circle r are given as θ=2πr=4000+200 milesr=4...

Q: Trigonometry Question

A: Find the solution below

Q: Show that 2 cis 30 degree and 2 cis (-30 degree) are conjugates.

A: We have to show that 2 cis 30° and 2 cis -30° are conjugates. We know that cis θ=cos θ+i sin θ and w...

Q: Use the given information and a calculator to find theta to the nearest tenth of a degree if0 degree...

Q: Find the exact value of each of the following. tan 315 degree

A: tan 315

Q: Use a calculator to help write each complex number in standard form. Round the numbersin your answer...

A: The complex number in the form a+ib , where is real part and b is imginary part.

Q: Determining Quadrant(s) for a PointIn Exercises 15–20, determine the quadrant(s)in which (x, y) coul...

Q: find the remaining trigonometric functions of theta based on thegiven information. tan theta = a/b w...

A: Given: tanθ=ab, where a and b are positive We know that value of tanθ is positive in first and third...

Q: Find all solutions in radians using exact values only. sin 2x cos 3x + cos 2x sin 3x = 21

A: some trigonometric formulascosA+B=cosAcosB-sinAsinBcosA-B=cosAcosB+sinAsinBsinA+B=sinAcosB+cosAsinBs...

Q: Graph one complete cycle of each of the following. In each case, label the axes accuratelyand identi...

A: Consider the given trigonometric function as y=cosx-π4

Q: In Exercises 1–4, write the complex number instandard form.1. 6 + √−4 2. 3 − √−253. i2 + 3i 4. −5i +...

A: We have to write the complex numbers in standard form: 1. 6+-42. 3--253. i2+3i4. -5i+i2 We know that...

Q: If 0 0 , A , 90 0, then A/2 terminates in which quadrant?

A: Given: A is an angle such that 0°≤A≤90° To determine: In which quadrant A2 terminates?

Q: Find the value of the variable in the isosceles trapezoid, 60° (2x+10)°

Q: Applying Trigonometric Identities In Exercises39 and 40, use the given function value and thetrigono...

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

Finding the Central Angle In Exercises 53 and 54,
find the radian measure of the central angle of a circle of
radius r that intercepts an arc of length s.
53. r = 80 kilometers, s = 150 kilometers
54. r = 14 feet, s = 8 feet

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Solution

VIEW

Step 2; Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ratios$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions

True or False? In Exercises 71–74, determine whether the statement is true or false. Justify your answer. The difference between the measures of two coterminal angles is always a multiple of 360 when expressed in degrees and is always a multiple of 2#35;960; radians when expressed in radians.
Finding the Central Angle In Exercises 53 and 54, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s . r=14feet, s=8feet
To determine the angle of elevation of a star in the sky, you align the star and the top of the backboard of a basketball hoop that is 5 feet higher than your eyes in your line of vision (see figure). Your horizontal distance from the backboard is 12 feet. What is the angle of elevation of the star?
Converting from Radians to Degrees In Exercises 37 and 38, convert each radian measure to degree measure. Do not use a calculator. (a) 32 (b) 76
Writing When the radius of a circle increases and the magnitude of a central angle is held constant, how does the length of the intercepted arc change? Explain.
Converting from Degrees to Radians In Exercises 35 and 36, convert each degree measure to radian measure as a multiple of . Do not use a calculator. (a) 120 (b) 20
Estimating an Angle In Exercises 7-10, estimate the angle to the nearest one-half radian.
Finding Arc Length In Exercises 51 and 52, find the length of the arc on a circle of radius r intercepted by a central angle . r=15inches, =120
Sketching Angles In Exercises 13 and 14, sketch each angle in standard position. (a)52(b)4
Using Radian or Degree Measure In Exercises 1-4, (a) sketch the angle in standard position, (b) determine the quadrant in which the angle lies, and (c) determine two coterminal angles (one positive and one negative). 110