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Limit of Trigonometric Function : L'Hopital's Rule

Lim of theta as theta approaches zero of (cos theta - 1) / sin theta Please provide a detailed, step-by-step solution so that I can understand what is happening and will be able to solve similar problems in the future on my own. Thank you.

Trigonometry : Word Problems

Q1. A glass crystal sculpture is made in the shape of a regular octagonal prism with 10 cm sides. Each of the lateral faces is square. To avoid breakage in shipment, the piece is padded with plastic foam beads when it is packed in its square-based rectangular box. The layer of beads must be at least 1 cm thick on all sides of

Trigonometry and vectors

A force of 800 lbs acts in an upward direction of 40 degrees with the floor. Draw this force as a vector and determine its horizontal and vertical components.


A handicap ramp is 5.26 meters above the ground. What will the length of the ramp if it makes an angle of 23 degrees with the floor?


A length of rope 168 feet stretches from a bolt in the floor to the peak of an 87 foot radio tower. What is the distance from the floor at the radio tower base to the bolt? What angle does the rope make with the floor?

Measure Height of Mountain : Angle of Elevation

To measure the height of a mountain a surveyor takes two sightings of the peak at a distance of 900 meters apart on a direct line to the mountain (see attached picture). The first observation results in an angle of elevation of 47 degrees, whereas the second results an angle of elevation of 35 degrees. If the transit is 2 meters

Trigonometry : Solve the Triangle

Solve the triangle, if possible. B = 24.4° C = 102.9° b = 38.62 Which is the correct answer? A = 50.7°, a = 93.13, c = 76.37 A = 50.7°, a = 91.13, c = 74.37 A = 52.7°, a = 76.37, c = 93.13 A = 52.7°, a = 74.37, c = 91.13

Applications of Trigonometry and Vectors

Please see the attached file for the fully formatted problems. 1. Find the indicated part of each triangle ABC. C = 118°, b = 130km, a = 75km; find c The correct answer to this problem is 180 km how did they come up with that answer? 2. Height of a Balloon: The angles of elevation of a balloon from two points A and B on

Solving Equation for a Given Interval

Solve the equation for the interval [0, 2л). sin^2 x - cos^2 x = 0 Which is the correct answer? x = л/4, л/3 x = л/4, 3л/4, 5л/4, 7л/4 x = л/4 x = л/4, л/6


Find the exact value, given that sin A = -4/5 with A in quadrant IV tan 2A Which is the correct answer? - 7/24 24/7 - 24/7 7/24


Solve the equation for solutions in the interval [0, 360). tan 4x = 0 Which is the correct answer? x = 33, 57, 147, 237, 327 x = 0, 90, 180, 270 x = 0, 45, 90, 135, 180, 225, 270 x = 0, 45, 90, 135, 180, 225, 270, 315

Inverse Circular Functions and Trigonometric Equations

1. Solve csc^2θ - 2 cot θ = 4 for solutions over the interval [0°, 360°]. Express approximate solutions to the nearest tenth of a degree. Could you please show me step by step to see how to get the correct answer? The correct answers are (18.4°, 135°, 198.4°, 315°)


Factor the trigonometric expression. Which is the correct answer? sin2x + sin2x cot2x cot2x - 1 sin2x + 1 cot2x + 1 1


Give the amplitude or period as requested. Which is the correct answer? Amplitude of y = 4 sin x 4л л/4 4 2л

Trigonometric proofs

1) Prove from the unit circle that sin²⊖ + cos²⊖ = 1. Using the result describe the equation for which x = 3 + 2cos⊖, y = 1 + 3sin⊖. 2) Using problem one simplify sin²⊖/(1 + cos⊖) + sin²⊖/(1 - cos⊖)

Trigonometric Identities

If you would please give me each step to solve these problems so I can get a better understanding how to solve these types of problems would be very helpful. Thanks. Graph each expression and use the graph to conjecture an identity. Then verify your conjecture algebraically. 1. sec x - sin x tan x Verify that each equat

Trigonometry : Period, Amplitude, Range, Y-intercept and Phase Shift

Develop the solutions for the following problems: 1.) Graph the function y = -1 + 2sin(x + π) over a 2-period interval. a. What is it's period? b. What is its amplitude? c. What is it's range? d. What is the y-intercept of it's graph? e. what is it's phase shift? 2.) The formula for the up and down motion o