Trigonometry

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...

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).

Hello. I am a pipe fitter and would like some help learning how I would calculate plotting ordinances on the steel tube to cut and fit to the contour of the pipe and the steel plate. 

Hello, thank you to anyone looking at this problem. I recently took a career changing test and did not pass. One problem I'd like to be prepared for next time involves a guywire connected to the top o...

Good morning, I need help to answer question 3 and 4.also to give a drawing of SFD and BMD with information.thank you.

Hello, please could someone help my with math as I am a little stuck. thank you

Say you have a triangle with internal angles of 62°, 48° and 70° and an internal area of 250m^2 how would you solve this?Thanks!

The problem is in the files attached.I have been given the coordinates of the raindrops both start and end.My question is how do I obtain the angle, and after that how do I arrange the equation to get...