sines

1. Problem #20: Sum of Sines

We haven't done a Trigonometry problem in a while, so here we go! Evaluate: sin^4 \left ( \frac{\pi}{8} \right ) + sin ^4 \left ( \frac{3 \pi}{8} \right ) + sin ^4 \left ( \frac{5 \pi}{8} \right ) + sin ^4 \left ( \frac{7 \pi}{8} \right ) -Dan
2. reciprocal form Of law of sines . question

Hello i am a bit confused when it comes to this law. How do i know when the reciprocal form is to be used And how do i know when its not to be used? If anyone could make an example. Thanks
3. Applying the Laws of Sines or Cosines

Solve the triangle. A = 19°, C = 102°, c = 6 choices are B = 31°, a ≈ 18, b ≈ 15.8 B = 59°, a ≈ 2, b ≈ 5.3 B = 59°, a ≈ 18, b ≈ 15.8 B = 59°, a ≈ 18, b ≈ 5.3
4. Law of Sines

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. B = 49°, a = 16, b = 14 Choices are A = 30.4°, C = 100.6°, c = 18.2; A = 149.6°, C = 79.4°, c = 18.2 A = 30.4°, C = 100.6°, c = 10.7; A = 149.6°, C = 79.4°, c = 10.7 A = 59.6°, C = 71.4°...
5. Applying the Laws of Sines or Cosines

Solve the triangle. B = 36°, a = 41, c = 17 choices are b ≈ 29, C ≈ 20, A ≈ 124 b ≈ 44, C ≈ 20, A ≈ 124 b ≈ 29, C ≈ 121, A ≈ 23 b ≈ 44, C ≈ 24, A ≈ 120
6. Law Of Sines

Using Law of Sines for the ambiguous case: SSA : Given the triangle with the following sides: A = 25 degrees, a = 8 cm, and b = 15cm , we begin by drawing a "vague triangular diagram": Step 1: Find the value of h ( this determines how many triangles you will have) : Step 2: Draw in the side...
7. Law of Sines

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65 degrees East, and the two towers are 30 km apart. A fire spotted by rangers in each tower has a bearing of N 80 degrees East from Pine Knob and S 70 degrees E from Colt Station. Find the distance of the fire from...
8. Use the law of sines to deduce the law of tangent

Use the law of sines to deduce the law of tangents for triangle ABC: (a-b)/(a-b) = (tan(1/2)(A-B))/(tan(1/2)(A-B)) I've put a lot of thought into this homework problem and I hardly even know where to begin. I've attended every class and done all of the homework and none of this seems familiar...
9. Sum of Product of Sines

Hello, I'm trying to show that \sum _{j=1}^{N-1} \sin \left(\frac{j \pi y}{N}\right)\sin\left(\frac{j \pi k}{N}\right)=0, if y does not equal k (with y and k both being integers). I've tried using the trig identity for the product of sines. That gives \sum _{j=1}^{N-1} \left [\cos\left (\frac{j...
10. Solving Vector Triangles (Law of Sines and Cosines possibly)

Hey all, I really don't know where to begin this problem. Three vectors, Vector AO is 400 in magnitude and direction going in -x from point A to O. (or can rearrange I believe to make another triangle piece) Vector AB is unknown going from point A to B. Vector AC is 525 in magnitude going from...
11. complex algebra? series sum of sines or cosines

how do i calculate the sum of each of these series? sin(A) + sin(A+B) + sin(A+2B) + sin(A+3B) .... + sin(A+(n-1)B) cos(A) + cos(A+B) + cos(A+2B) + cos(A+3B) .... + cos(A+(n-1)B) please show step by step how to do it, not just the answer.
12. Surveying Property (Law of Sines)

can someone help me sketch out this? I tried by myself but always end up with the wrong answer.
13. Law of Sines Application Help

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi. apart, to be 32 degrees and 48 degrees as shown in the figure. a) Find the distance of the plane from point A. b) Find the elevation of the plane. imgur: the simple image sharer...
14. Formula product of sines

Does anyone know how to prove this formula? 2^{n-1}\prod_{k=0}^{n-1}\sin(x+\frac{k\pi}{n}) = \sin(nx) All suggestions, ideas are welcome. Below you find my unsuccessfull attempt using complex numbers. When you convert it to complex numbers the equality can be rewritten as...
15. The product of sines and the product of cosines of (k\pi)/(2n+1) for 0<k<n+1

I have to prove the following identities: \prod_{k=1}^n \cos\frac{k\pi}{2n+1}=\frac{1}{2^n} \prod_{k=1}^n \cos\frac{k\pi}{2n+1}=\frac{\sqrt{2n+1}}{2^n} The suggestion is to prove and use this: \sum_{k=0}^{2n}z^k=\prod_{k=1}^n \left (1-2z\cos\frac{2k\pi}{2n+1}+z^2\right ) for z\in\mathbb{C}...
16. Another proof with Law of Sines

Let p and q be the radii of two circles through A (with A being a point on Triangle ABC), touching BC at B and C, respectively. Prove the pq = R squared. (R is the radius of the circle circumscribed around ABC). I have been trying over and over to do this problem, and I just can't get it.
17. Proof using Law of Sines

For any triangle ABC, even if B or C is an obtuse angle, a = b cos C + c cos B. Use the Law of Sines to deduce the "addition formula" sin (B + C) = sin B cos C + sin C cos B I got most of it but can't figure out the end. I replaced b with 2R sin B and c with 2R sin C so a = 2R sin B...
18. Proof using Law of Sines

For any triangle ABC, even if B or C is an obtuse angle, a = b cos C + c cos B. Use the Law of Sines to deduce the "addition formula" sin (B + C) = sin B cos C + sin C cos B I got most of it but can't figure out the end. I replaced b with 2R sin B and c with 2R sin C so a = 2R sin B...
19. the zero of the third derivative of iterated sines

Let f_n\colon[0,\pi/2]\longrightarrow[0,1] for n=0,1,... and \begin{cases}f_0=\sin\\f_{n+1}=\sin\circ f_n\end{cases} I would like to prove that for n=1,2,... the third derivative f_n^{(3)} has a unique zero in (0,\pi/2). I thought calculating the third derivative and solving an equation...
20. Ambiguous case using law of sines

Hello, here is the data I am given to work with: Angle A=30 deg Side a=3 Angle B=unknown Side b=unknown Angle C=unknown Side c=4 So I know that I can take the 3/sin30 = 4/sinC Rearranging that, I am left with SinC = Sin(30)(4)/3 which can further be simplified to 41.81 deg. So does having...