Trigonometry. . show your solution!?
cos(105) = -√(1 + cos(210))/2) .............. cos(210) = -√3/2 = -√(1/2 - √3/4) = -√(2 - √3) / 2 Answer: -√(2 - √3) / 2 tan(22.5) = sin(45) / (1 + cos(45)) ........ sin(45) = cos(45) = √2/2 = √2/2 / (1 + √2/2) = √2 / (2 + √2) = √2 -1 Answer: √2 - 1 If tan(θ) = -7/24, then tan(θ/2) = sin(θ) / (1 + cos(θ)) = (-7/√(7² + 24²)) / (1 + 24/√(7² + 24²)) = -7/49 Answer: -7/49
Where can I find S.L Loney’s Trigonometry Solutions?
Conceptual Trigonometry Part I: A Companion to S. L. Loney's Plane Trigonometry Part I by Chandra Shekhar Kumar
General Solutions in Trigonometry?
First step is to substitute 2x-45 = θ. Now we have sin(θ) = √3/2. Since the sin function is the y-value as you go around the unit circle, where on the unit circle is the y-value √3/2? Two places: θ = 60 and θ = 120. But we also know that the sin function repeats every 360 degrees (or 2 pi radians) so the general solution is θ = 60 + 360n and θ = 120 +360n, where n is an integer. Finally, we now just have to substitute back to get our answer in terms of x. That is, 2x - 45 = 60 + 360n and 2x - 45 = 120 +360n. Do the algebra on each to solve for x and you get x = 105/2 + 180n and x = 165/2 + 180n. Since they only want values of x on [0,360] you have to plug in values of n starting at 0 until you exceed 360. The answers are 52.5, 232.5 (from the first equation with n = 0 and 1) and 82.5, 262.5 (from the second equation with n = 0 and 1).
What is principal and general solutions in trigonometry?
Principle solution of trigonometric equation restrict the solution in the Range 0 <= x < 2π.General Solution is the expression involving some integer ,say K , which gives all solution a trigonometric equation .To derive the general solution , we use the periodicity of trigonometric functions .Period of Sin(x) = 2π Cos(x) = 2π Tan(x)=πFor general solution , we also use some Standard results.1) if Sin(x) = Sin (y) => x = nπ +(-1)^n * y , where n is an integer.2) if Cos(x) = Cos(y) => x = 2nπ y + - y , where n is an integer.3) if x & y are not multiple of π/2 Then Tan(x) = Tan(y) => x = nπ + y , where n is an integer .
Where can I find a link for The Solutions of Plane Trigonometry, Part I, by S. L. Loney?
Loney-Plane_trigonometry.djvu ( i have not been able to find out any PDF link to download the file)solutions : Complete solution to co-ordinate geometry [by] S.L. Loney try this website ( i have not verified the website myself) lastly, i will suggest you to solve all the problems yourself, don't rely on solution book.
HELP! What is wrong with this solution (Trigonometry)?
You eliminated one solution when you divide both sides by sinx. The answers will be in (0, 2Pi) interval sinxtanx = sinx sinxtanx - sinx = 0 sinx(tanx - 1) = 0 sinx = 0 when x = 0 or Pi tanx - 1 = 0 tanx = 1 x = Pi/4 or 5Pi/4
I need a worked out solution to this trigonometry question PLEASE!?
Solve the problem. Snell's Law states that c1/c2 = sin theta1/ sin theta2. Use this law to find the requested value. If c1 = 3*10^8, c2 = 2.33 * 10^8, theta2 = 34 degrees find theta1. Round your answer to the nearest degree.