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# Trigonometry

### Trigonometry to Determine the Values

1. The graph of a tangent function is given. Select the equation for the following graph: y = tan , y = tan( x +π ), y = tan x, y = tan 2. Graph two periods of the given tangent function. y = 2 tan 2x 3. Graph two periods of the given cosecant or secant function. y = 3 sec x 4.

### Pythagorean Theorem application

A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

### Calculate the angular speed of the engine in radians per second

1.) The engine of a sports car rotates at 5,000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2&#61552; radians = 1 revolution. 2.) Convert -60° to radians. Express the answer as a multiple of &#960; 3.) Draw the following angle in standard the position: 4.) In which q

### Triangles and squares

Draw several kinds of triangles including a right triangle. Draw a square on each of the sides of the triangles. Compute the areas of the squares and use this information to investigate whether the Pythagorean Theorem works for only right triangles. Use a geometry utility if available.

### Solving an Integral Example Problem

I need help finishing the following problem: Integral cos^5t dt =Int cos^2t*cos^2t*cost dt =int(1-sin^2t)(1-sin^2t)cost dt =Int(1-2sin^2t+sin^4t)cost dt =Int cost dt -2*Int sin^2t cost dt + Int sin^4t cost dt

### 2D diagrams vectors

1. A plane sets a course to fly with a ground speed of 200 km/h due east while climbing at an angle of 14 degrees. Upon takeoff, it is affected by a 20 km/h wind blowing directly north, as shown in the diagram below. (Please see the attached file for the diagram) a) Model this problem using two 2D diagrams (&#8710;ABC and

### Two trigonometry problems

PLEASE SHOW ALL WORK..... 1. A bicycle tire has a diameter of 20 inches and is revolving at a rate of 10 rpm. At t =0, a certain point is at height 0. What is the height of the point above the ground after 20 seconds? 2. The sun always illuminates half of the moon's surface, except during a lunar eclipse. The illuminated

### Trigonometric ratios of heights and distances

A pilot in a helicopter sights an ambulance heading toward an accident scene. He measures the angles of depression to the ambulance and the accident to be 21 degrees and 15 degrees, respectively. If the helicopter is 4000 ft from the ambulance, how far does the ambulance have to travel to get to the accident?

### Trigonometry problems

E= {(x,g(x)): (-3,-7), (-1,-3), (0,-1), (2,3), (4,7)} Write the rule for g-1(x): Show that csc[arccos x] = 1/ root(1-x2): sin 0=.4910; angle 0 = sec(-38 degrees 22') = If F(x) = log5 2x, find F-1(x)._________ Find (a) an upper limit and (b) a lower limit for the zeros of the function P(x)....zeros= -3/2, -r

### number of protons, neutrons, and electrons

Parallel Exercises An electron with a mass of 9.11x10-31 kg has a velocity of 4.3 106 in the innermost orbit of a hydrogen atom. What is the de Broglie Wavelength of the electron? An electron wave making a standing wave in hydrogen atom has a wavelength of 8.33 x 10-11 m. If the mass of the electron is 9.11x10-31 kg. what

### Pythagorean Theorem Example

Find the length of the diagonal of a rectangular billboard whose sides are 5 feet and 12 feet. Note that the length of the diagonal of a rectangle with length = a and width = b is given by the Pythagorean Theorem c^2 = a^2 + b^2.

### Pythagorean Triples Equations

The Numbers 3,4, and 5 are called Pythagorean triples since 3^2 + 4^2 = 5^2. The Numbers 5,12, and 13 are also Pythagorean triples since 5^2 + 12^2 =13^2. Can you find any other Pythagorean triples? Actually, there are alot of formulas that will generate as infinite number of Pythagorean Triples. Make sure you select at least

### Trigonometry word problem: building a wheel chair ramp

A contractor is building a wheelchair accessibility ramp (see figure) for a business. Using your knowledge of right-triangle trigonometry, help advise him how to create a ramp whose dimensions will meet the specification needed that will allow wheelchair accessibility. Talk about the procedure the contractor will need to follow

A 30-foot ladder is leaning up against a roof that is 20 feet above the ground. How far from the building is the foot of the ladder? What is the angle between the ladder and the ground? A few words on syntax when dealing with trigonometry: We will use upper-case letters for the functions, and enclose the argument in ( ). Use

### Trigonometry Resultant Magnitude

1. Two forces P and Q are applied as shown at point A of a hook support. Knowing that P=75 N and Q = 125 N. Determine by trigonometry (a) the required magnitude of the force Q if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R. 2, Solve by trigonometry. Two forces are app

### The corresponding value of t

A very long rectangular piece of paper is 20 cm wide. The bottom right hand corner is folded along the crease so that the corner just touches the left hand side of the page. How should this be done so that the crease is as short as possible?

### RHS Theorem (Right-angle-Hypotenuse-Side)

Please help me with the following problem: a) Prove that two Pythagorean Triangles with the same area and equal hypotenuses are congruent. b) Find two Pythagorean triangls with the same area. Please show all work. Thanks in advance for the assistance.

### Pythagorean Triangles Programs

Please help me with the following problem: a) 3^2 + 4^2 = 5^2 20^2 + 21^2 = 29^2 119^2 + 120^2 = 169^2 To find another such relation, show that if a^2 + (a+1)^2 = c^2, then (3a+2c+1)^2 + (3a+2c+2)^2 = (4a+3c+2)^2. (b) If a^2 + (a+1)^2 = c^2, let u=c-a-1 and v=(2a+1-c)/2. Show that v is an integer and tha

### Pythagorean Triangles Areas

1. Find two pythagorean triangles with the same area. Can you find any more with the same area? 2. Prove that two Pythagorean triangles with the same area and equal hypotenuses are congruent.

### Pythagorean Triangles

The question I need help with is the following: How many Pythagorean triangles (primitive or not) can you find with hypotenuse 1105? Please show all work. Thanks in advance for the help.

### Problems with Pythagorean Triangles

I need help with this problem. Here it is: Bhascara found a right triangle whose area is numerically equal to the length of its hypotenuse. Show that this cannot happen if the triangle has integer sides. Please be detailed as possible. I appreciate your help.

### Pythagoras Theorem to Find Length of Ladder

A man is placing a ladder against a tree to climb to the top. The ladder is placed 3 feet from the base of the tree. The height at which the ladder will reach the tree is 4 feet. Use the Pythagoras Theorem to find the length of the ladder.

### 25ft ladder, 10ft from base of sign, what point will the ladder touch the sign. then using the ground 15ft from the base,what point will the ladder reach the sign.

20ft billboard, the bottom which is 15ft off the ground. the painter has a 25ft ladder. from the 10ft from the base at what point will the ladder reach the sign? from the 15ft from the base of the sign, at what point will the ladder reach?

### Pythagoras Theorem: Billboard and Ladder Problem

A billboard painter has been assigned the task of changing the advertisement on a 20 ft billboard, the bottom is 15ft off the ground, two other sites under the sign,one is 10ft from the base the other is 15ft from the base. If the painter uses the patch that is 10ft from the base, what is the length of the ladder required to rea

### six trigonometric functions

Show work 130. An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 1 sec. 94. Use identities to solve each of the following. Find sin 0, given that cos 0 = 4/5 and 0 is in quadrant IV. 72. Find exact values of six trigonometric functions

### Trigonometric Identities: Example Problem

Trigonometric Identities: The assignment given is to prove that sin θ/(1 - cos θ)] - [(1 + cos θ)/sin θ] = 0. In other words, we want to prove that [sin θ/(1 - cos θ)] = [(1 + cos θ)/sin θ]. Please see attachment for full details of the problem.

### Remote Controlled Robot Following A Path

Use a protractor and graph paper to map out the following path for the turtle. Be sure to scale for any distances. -5 meters at a bearing of 110-then 8 meters at a bearing of 210-the 9 meters at a bearing of 260 How far is the turtle form the starting point? What bearing will return the turtle to it's starting position?

### Pythagorean Triples

1. What is the rule that allows you to find ALL the Pythagorean Triples that are possible. 2. You should then find 5 different examples of Pythagorean Triples using this rule. You must show IN DETAIL how you created the 5 examples by the using the rule. It is not sufficient to simply list the Pythagorean triples without fu

### Heron's formula

Please see the attached file Thank-you

### Trigonometric Equations Expressions

Given that x = 3sin theta and y = 4cos theta,express x + y in the form R sin (theta + alpha) giving alpha in radians correct to 4 decimal places and hence solve the equation, 3sin theta + 4cos theta =1.2 giving your answers in radians in the range -Pi to +Pi