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Trigonometry

Dimensions of the Door

Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilize the door by attaching a steel cable diagonally. If the cable measures sq 194/2 ft, what are the dimensions of the door?

Trigonometry Questions

Give a polar equation for the curve whose graph is a vertical line that passes 3 units to the right of the origin. A parabolic reflector has a width w=20 feet and a depth d =4 feet. how far from the center will the focal point be? See attached for third question

Trigonometry Questions

Solve the system x-2y+z=-1 and system x+2y-2z=-1 -2x+3y+2z=4 x+3y+z=10 2x+y+3z=9 2x+6y+2z=20 Find the maximum value of c=6X + 5y on the region determined by the constaints 3x+2y+>or equal to 20 2< or equal to X<or equal to 8 1< or eq

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

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

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

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

Trigonometry Word Problems for a Surveyor

1. A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 130 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 55(degrees). What is the distance between the piling and the p

HOW FAR IS THE FIRE FROM B?

LOOKOUT STATION A is 15 km west of station B. THE BEARING FROM A TO A FIRE DIRECTLY SOUTH OF B IS 37 DEGREES AND 50'E. HOW FAR IS THE FIRE FROM B?

Cartesian coordinates

1. A boat sails at a constant speed in a straight line. its position at time S is (30S- 300,10S +500). in the water there are two buoys, A and B. at positions A- (7100,2800) and B - (125700,42500). a) write an expression in terms of S that is the square of the distance between the boat and buoy A at time S, simplify the answe

Trigonometry and Triangles Word Problems

Points A and B lie in a direct line on level ground to the west of a mountain which is known to be 1 mile high. The angle of elevation from point A to the mountain top is 4 degrees and the angle of elevation from point B to the mountain top is 6 degrees. Find the distance between points A and B.

Deriving trigonometric identities.

Use trigonometric identities to derive the following identities: a.) sin^2x+cos^2x=1 b.) sin2x=2sinxcosx c.) cos2x=cos^2x-sin^2x d.) cos2x=2cos^2x-1 e.) cos2x=1-2sin^2x

Limit of cosine using epsilon/delta definition

I am having difficulty using the epsilon/delta definition....even difficulty when not using it. There's a problem which reads as follows: find the limit as x approaches 0 of (cosx-1)/x^2. The main reason as to why I am having difficulty without using the epsilon/delta definition is because I simply am confused what to do when

Pythagorean Theorem

Find the side length x for a right triangle..when its sides are 7 and 11. Round to the nearest tenth

Important information about application of trigonometric functions in real life

As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representations u

Trigonometric Limit

Find the trigonometric limit of the following (please show work) lim (x - tan2x)/sin2x x--> 0

Finding the angle made by an arc at the center of the circle

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s , while the radius r = 1 meter and s = 300 centimeters. Find a positive angle less than 360degrees that is co terminal with the angle - 822degrees The minute hand of a clock is 5 inches long. How far does the tip of th

Trigonometry Word Problems

13) A rocket tracking station has two telescopes A and B placed 1.3 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A r

Trigonometry and Geometry Word Problems

3) A building 210 feet tall casts a 90 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.) A) 66.40° B) 64.09° C

Trigonometry and Vector Components Word Problems

20. A small fire is sighted from ranger stations A and B. Station B is 1 .6 miles due east of station A. The bearing of the fire from station A is N40°E, and the bearing of the fire from station B is N5OW. How far, to the nearest tenth of a mile, is the fire from station A? 21. The magnitude and direction of two forces actin