Trigonometry

Calculate the derivative of this function

I am working on analyzing a specific segment of the sinusoidal curve, particularly the portion that is concave down. For this segment, I have two primary measurements I would like to determine: *The...

I include a screenshot of the question. Could you please explain how you got your answer.

Consider function y=2sin(3x-pi) 1.) Find the Amplitude.2.)Find the Period.3.)Find the Phase Shift.4.) Make a sketch of at least one period. Find and label 5 key points on a graph.Then use your result...

I've uploaded an image which contains the question.The answers are $-\frac{5\pi }{24} ,-\frac{\pi }{24},\frac{19\pi }{24},\frac{23\pi }{24} $ But I don't know how you get $\frac{19\pi }{24},\frac{23\p...

Hello,I would really appreciate some help understanding the derivation for x' and y' for Equation (1), Equation (2), and Equation (3). I recall that to convert Cylindrical Coordinates to Cartesian Coo...

The population of beavers can be modeled by a sine function f(x), where x is time in days. at t=0 the number of beavers is at its average of 100, the highest number is measured to be 125. The cycle st...

What is the domain and range of the function $f$ defined by  $f(x)=\frac{1}{1-\sin x}$?In my book the solution is the following:But I have some questions:1. The domain if $f$ is $\mathbb{R}$-$D$. The...

Hi All,I am building a robotoc bird and have drive mechanism with a gear that has a linkage attached to it at some distance (L) like in the picture (#2 and #3). I am trying to find the vertical compon...

We have two vectors AC and BD, coordinates for A are 1.5,4 and for C are 4,7.5, the only 4 known facts of BD are:B lies at a unknown location on vector ACX coordinate for D is 0BD magnitude is 2.5BD i...

Knowing the points a, b and the angle alpha, calculate the necessary angle beta to cover a known distance C, on the Y plane. The ab line segment is part of the triangle bisector.

Prove that $\sin^2(\pi/18)+\sin^2(5\pi/18)+\sin^2(25\pi/18)=3/2$.I believe the way im meant to solve this involves mainly the use of tried identities, and I have a strong feeling the triple angle iden...

I have an object that I need to rotate/reposition. I want to use a rotation matrix but because the x,y position of the object is determined by 6 values ( lets say x = 435, 435, 510 and y= 500 ,456, 54...

I am a P.E. teacher and haven't done any trig in a decade... I am trying to find the internal angles of the frame of my bike to get a custom bag made for the frame. I have the measurements of the inte...

1. A bee, after collecting nectar from a flower, flies in a straight line in the bearing S$31^\circ$ W. After flying 2.3meters, it lands on another flower, then, after collecting more nectar, it flies...

Hello !I was wondering if there would be an equation for this sort of a problem or if the solution might need to be brute forced by approximation. example image: https://imgur.com/ql9tAxEThere is a re...

There is a right triangle ABC in the plane, of which angle C is a right angle. If the the line segment through A to the midpoint of BC is on the straight line x+y=0, the line segment through B to the...

Hello!Here is a trig problem I simply do not have the knowledge to solve, please help! Here are the rules:TASK: Create a complex or simple polygon with the smallest possible perimeter adhering the fol...

I've attached a file with the expression screenshooted. The answer is supposed to be (1 + 2 sin x cos x)∧ −1. But I can't arrive at it. Help would be appreciated. 

If two weights, weight 1 = 40lbs, weight 2 = 30lbs, are fastened together and placed on inclined planes (30 degrees for weight 1, and 40 degrees for weight 2), which way will the slide? (Left or right...

A ship leaves port (position 44.67°N, 63.58°W), starting due east and continuing on the great circle. Find its position after it has sailed 1000 nautical miles. Find its direction after it has sailed...

Solve the following sherical triangle a = 122°18' b = 88°21', C = 100°16'.Note that a is the length of a side provided as an angle, while C is an angle of the spherical tirangle. Solving the tirangle...

In a right spherical triangle with C = $\pi /2$ ; , you know angles A and B . How do you find the side b? Provide the formula using Napier's Pentagram.

Calculate the distance along the great circle between Vancouver (49°15'N, 123°6'W) and Palma de Mallorca (39°34'N, 2°39'E).