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Trigonometry

Trigonometry Problems

A triangle plot of land has sides of lengths 130 feet, 110 feet, and 100 feet. Approximate the smallest angle between the sides. A radar operator sights two objects, one at a distance of 7 miles and the other at a distance of 12 miles. If the angle between the sightings is 35 degrees, how far apart are the object? A

Derivatives : Trigonometry Rate of Change Problems

1.) A fugitive is running along a wall at 4.0m/s. A searchlight 20m from the wall is trained on him. How fast is the searchlight rotating at the instant when he is 10m from the point on the wall nearest the searching? 2.) A balloon is rising from the ground at the rate of 6.0m/s from a point 100m from an observer, also on the

Verify a Trigonometric Identity

Prove that sin2 x + cos2 x = 1 using only this information : Cos x = (e^jx + e^-jx)/2, sin x = (e^jx - e^-jx)/(2j) See attached file for full problem description.

Trigonometry problem: latitude and nautical mile

A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. a) Find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code). The latitude fo

Trigonometry Exam (20 Problems)

Please see the attached file for all of the fully formatted problems. 1. You have calibrated your voltmeter so that you know a meter reading of 10 V is actually 10.2 V and a reading of 15 V is actually 15.6 V. What is the actual voltage when your meter reads 12.3 V? (1) 11.9V (3) 12.3 V (5) 13.1 V (2) 12.1 V (4) 12.7 V (6

Graphs of Trigonometric Functions and Mean Value

(a) Sketch the graph of y = cos X in the range - π ≤ X ≤ π. π="pi" Hence sketch the graph of y = cos X in the same range. (b) Find the mean value of y = cos X in the range - π ≤ X ≤ π

Trigonometry Word Problems

What is the length of the diagonal of a rectangular billboard whose sides are 5 meters and 12 meters? keywords: hypotenuse, Pythagorean

Trigonometry Word Problem - Football Game

Suppose at kickoff of a football game, the receiver catches the football at the left side of the goal line and runs for a touchdown diagonally across the field. How many yards would he run? (A football field is 100 yards long and 160 feet wide).

Trigonometry and Heart Rates

#120 Digging up the street. A contractor wants to install a pipeline connecting point A with point C on opposite sides of a road. To save money, the contractor has decided to lay the pipe to point B and then under the road to point C. Find the measure of the angle marked x in the figure for exercise #120 on page 161.

Trigonometric Identities

Match sin x sec x with one of the following: ? csc x ? tan x ? sin x tan x ? sin x cot x Use trigonometric identities to factor and simplify the following: ? sin2 x * sec2 x - sin2 x

Trigonometric Functions

Which one of the following trigonometric functions of x is not correct? Which one of the following trigonometric functions of x is not correct given that sin x > 0 and sec x = -2? ? csc x = ( 2 sq rt 3) / 3 ? cos x = - 1 / 2 ? cot x = - ( sq rt 3 ) / 3 ? tan x = - ( sq rt 3 ) / 2

Trigonometric Identities

Match sec4 y - tan4 y to one of the following: ? csc y ? sec2 y+ tan2 y ? 1+ tan y ? csc y x cot y

Trigonometric Identities

Prove the identity of this problem. sin x - sin y x - y -------------- = tan (--------) cos x - cos y 2 keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Transformations of Trigonometric Functions

Here is an example of the problem that I am working on at this time. I need to know how to list the transformation needed to change the graph of f(t) into the graph of g(t). f(x) = sin t; g(t)= -3 sin t

Solving Trigonometric Equations

Solve each equation for solutions over the interval [0,2π) sin x + 2 = 3 2 sec x + 1 = sec x + 3 Solve each eqation for solutions over the interval [0º,360º) cos²Θ = sin²Θ + 1 4cos²Θ + 4cosΘ = 1 See attached file for full problem description.

Solving Trigonometric Equations

For the following trigonometric equation, find all solutions in the interval 0≤ θ ≤ 360 2 cot θ sec θ = 3

Proving Identities

We have been working on proving identities and it's a subject I just can't get my brain around. A few of the problems we've been given have made me stumble. cotx/1+tan(-x) + tanx/1+cot(-x) = cotx + tanx +1 I figure on this one, with using identities, I can get: cotx/1-tanx + tanx/1-cotx = cotx + tanx +1 But I can't g

Trigonometry : Graphs, Asymptotes and Phase Shifts (13 Problems)

1. If sin(alpha)=1/5 where alpha is in quadrant II, find the remaining five trigonometric functions of alpha. 2. Given that sin(alpha)= -2/3 and cos(alpha)= -root5/3>0, find the remaining four trigonometric functions. 3. Sketch a graph of y=3cos(2theta+pi) using either transformations or the "5 key points" method. Be