Trigonometry Answers

Sin2+ sin3

Let 0<θ<2π, θ

I was given a data set of the daylight hours of a couple of cities (Tokyo,Yakutsk and Adelaide). Thanks to this article, I did not need to plot the graphs on Desmos to calculate the amplitude. I also have a question. How does the amplitude vary with the geographical location of the cities? What is the relation? Thank you!

Problem C

Determine the numerical value of the following expression without the use of a calculator: 

problem is found on the website below

https://docs.google.com/viewerng/viewer?url=https://iymc.info/docs/IYMC_Qualification_Round_2021.pdf

1. Two lighthouses A and B are 25km apart and A is due west of B. A submarine S is on a bearing of 137degrees from A and on a bearing of 170degrees from B. Find the distance of S from A and the distance of S from B.

2. In the triangle PQR, PQ= 7cm, PR= 8cm and QR= 9cm. Find angle QPR.\

3. Find the smallest angle in a triangle whose sides are of length 3x, 4x and 6x.

4. Shop Y is 9km due North of shop Z. Shop X is 8km from Y, 5km from Z and somewhere to the west of line YZ.

a) Draw the triangle XYZ and find angle YZX.

b) To improve sales, shop X is moved due to South until it is due West of Z. Find how far it moved.

Find the vectors that join the center of a clock to the hours 1:00, 2:00, and 3:00. Assume the clock is circular with a radius of 1 unit

tan x =1/2 and the terminal side of the angle is in the II quadrant ,then cos x =?