trigonometry

2. A trigonometric problem with the Laws of sine and cosine

Greetings, I'm having an interesting case where the solution of a certain angle cannot obtain the same result using the laws of sine and cosine for a triangle. I cannot understand why the answer doesn't match since from the perspective I'm getting of the problem, both laws can be used. In this...
3. Pretty basic Pythagorean & Trigonometry

Hi, It's probably gonna be a pretty simple thing to solve for you but I'm not that good in math so I'm really thankful for any help that you can bring me. Long story short (refer picture below): As you can see we have two circles forming two right angled triangles with a third one. The...
4. Trigonometry problems

(1) If z_1 \neq z_2 and z_1 , z_2 \in (0,\pi ). Prove that \: \sin\left(\frac{z_1 +z_2 }{2}\right) > \frac{\sin(z_1 ) +\sin(z_2 )}{2}. (2) Find all pairs (x,y) such that x^2 +2x\cdot \cos(xy)+1=0. (3) Find the number of solutions of the equation \sin(x)=\frac{x}{n} \; , where n\in \mathbb{N}...
5. How to simplify this expression involving a tangent of 70?

My situation is as follows. Can the expression from below be simplified using precalculus and plain by hand calculation without requiring a calculator? $$B=\sqrt{3} \tan 70^{\circ}- 4 \sin 70^{\circ}+1$$ What I attempted to do was to split the functions in a sum of $30^{\circ}+40^{\circ}$...
6. Quick Geometry and Trigonometry Questions

1. If a right triangle has equal legs, the hypotenuse divided by a leg is the square root of 2. If a right triangle has unequal legs, is it always true that the hypotenuse divided by the longer leg is less than the square root of 2 and the hypotenuse divided by the shorter leg is greater than...
7. Circle Trigonometry

The area of a circle is 15 cm^2 and the length of its arc is 3 cm. Calculate the radius of the sector and its angle. May somebody help please
8. How to calculate horizontal and vertical components by trigonometry?

A 75 N force is acting at an angle of 20 with the horizontal. Determine the horizontal and vertical components of this force.
9. Making a formula that finds the horizontal and vertical distance between two points t

I am making a Scratch 3.0 game. The shooter sprite is holding a gun slightly off-centre (see images), and I need the bullet to go to the end of the barrel of the gun before travelling forward (as so it would appear the bullet it leaving the gun). The issue is, to do this, I need to find the X...
10. Equation with cosines

Here is the equation. I tried using substitution and expanding the terms with the help of trigonometric identities but nothing has worked for me. Could you help me by solving it? Thank you very much.
11. Compound tangents questions

I was looking to solve this geometrical problem. I have a line which is subdivided so that the when it is intersected it creates tangents of equal lengths that are stacked upon each other. I'm looking to find a way to calculate the length of tangents (in red) that would divide n number of times...
12. A 1 unit by 1 unit triangle is impossible

If you have none maths you will have been taught about a triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to root 2. Root 2 never terminates-it does not stop but A 1 unit by 1 unit triangle is impossible- thus maths ends in meaninglessness...
13. Trigonometry nearing +/- infinities

What function might represent the greatest symmetry of a number line whereupon negative infinity approaches (or circumscribes) infinity? A complex circle?
14. Trigonometry identities

I need detailed solutions for the equation tan^2(x+45)=5 for 0<x<360 where 45 is in degrees.
15. Trigonometry

Given tan(x-y)=-2/3 and tanx=-1/2, find the value of a. tan y b. (x+y) for 0<x+y<360 please. I need all possible solutions.

Right so the question states that the volume of a triangular prism is 24cm cubed. it gave the length of the triangular prism as 5cm and the base of the cross sectional area 6. It wanted me to work out the height. So I converted it to algebra: (6*h/2) * 5 = 24cm^3 From there I went to: 6*h *...
17. GeoGebra and Limits at Infinity (Commands)

Hi guys! Would you help me with all the commands on GeoGebra that you know to graph Limits at Infinity? I'd really appreciate it. Thank you. :wink:
18. Can you help me to demonstrate these limits? [It's URGENT!!!!]

Hello! :wavespin: Thank you for bothering to help me with this.... I need you to please help me with these points of my calculus activity. ;) The subject is called Trigonometric Limits. The first one [A] has to be demonstrated using the sandwich theorem. And the second [F] has to be...
19. Trigonometry and a Convex Quadrilateral

Hey, I'm stuck in another math problem... sin A + sin B + sin C + sin D = 4 * sin(A+B)/2 * sin(B+C)/2 * sin(C+A)/2 "prove in a convex square ABCD the formula above" thanks!
20. Prove: (Sin B + sin C - sin A)/(sin A + sin C - sin B) = tan(B/2) . cot (A/2)

Hello everyone! I am preparing for a test and I got to this question in my coursebook. However, I'm not able to solve it. Can someone help me? I already tried using the sine law on the left side, the definition of tangens and cotangens on the right side. Nothing got me to prove it. Can...