# What is Trig: Definition and 1000 Discussions

The Renewables Infrastructure Group (LSE: TRIG) is a large British investment trust dedicated to investments in assets generating electricity from renewable sources. Established in 2013, the company is a constituent of the FTSE 250 Index. The chairman is Helen Mahy.

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1. ### How to Determine Correct Inverse Trig Angle?

I understand why certain inverse trig functions have two answers. Like for arcsin(0.5), it could be pi/6 or 5pi/6. I know both angles have the same sin value, that they're both on the same horizontal line on a graph of sin, I get all of that, but two questions about it: 1) In cases where...
2. ### I Practice With Proofs? (Algebra, Trig, and Calc)

I'm trying to brush up on my algebra, trig, and calculus, and one thing I know I was always weak on before was proofs. I was never sure what equations would suffice as "proof," and which equations did not. Maybe this is an inane question, and maybe there is a really simple answer to this. I...
3. ### A Trig functions and the gyroscope

Good Morning As I continue to study the gyroscope with Tait-Bryan angles or Euler angles, and work out relationships to develop steady precession, I notice that the trig functions cancel. I stumble on terms like: 1. sin(theta)cos(theta) - cos(theta)sin(theta) 2. Cos_squared +...
4. ### Another way to find trig identities

Using the identity's (1) (2) Gives, Why dose this elegant method work? Many thanks!
5. ### Proving trig identities -- Is the method related to the unit circle?

Why when proving trig identities, Do we assume that r = 1 from ## rcis\theta = r[\cos\theta + i\sin\theta]##? This makes me think that this is somehow it is related the unit circle. Note: I am trying to prove the ##cos3\theta## identity and am curious why we assume that the modulus is 1...
6. ### Find an equivalent equation involving trig functions

Rewrite the given equation, attempt 1: ##2\sin(x)\cos(x) + 2\sin(x) + 2\cos(x) = 0## ##\sin(x)\cos(x) + \sin(x) + \cos(x) = 0## ##\sin(x)(\cos(x) + 1) + \cos(x) = 0##, naaah, can't get any relevant out from here. Attempt 2: ##2\sin(x)\cos(x) + 2\sqrt{2}*\sin(x + \pi/4) = 0## ##\sin(x)\cos(x) +...
7. ### Comparing Hyperbolic and Cartesian Trig Properties

I came across this question; i noted that the hyperbolic trigonometry properties are somewhat similar to what i may call cartesian trigonometry properties... My approach on this; ##\tanh x = \sinh y## ...just follows from ##y=\sin^{-1}(\tan x)## ##\tan x = \sin y## Therefore...
8. ### I Adding trig functions with different amplitudes

The trig identities for adding trig functions can be seen: But here the amplitudes are identical (i.e. A = 1). However, what do I do if I have two arbitrary, real amplitudes for each term? How would the identity change? Analysis: If the amplitudes do show up on the RHS, we would expect them...
9. ### Differentiate ##f(x)=x\cos{x}+2\tan{x}: D/dx ##\tiny{2.4.2}##

##\tiny{2.4.2}## Differentiate ##f(x)=x\cos{x}+2\tan{x}## Product Rule ##[-x\sin{x}+\cos{x}]+[2\sec^2]\implies \cos{x}-x\sin{x}+2\sec^2x## mostly just seeing how posting here works typos maybe suggestions what forum do I go to for tikz stuff
10. ### Proof of the trig identities for half-angles

I was just checking this out the sin##\frac {A}{2}## property, in doing so i picked a Right-Angled triangle, say ##ABC##, with ##AB=5cm##, ##BC=4cm## and ##CA= 3cm##. From this i have, ##s=6cm## now substituting this into the formula, ##sin\frac {A}{2}##= ##\frac {1×3}{5×3}##=##\frac...
11. ### Solving for z in the Equation tan z = 1 + 2i

Find the values of tan-1(1+2i). We can use the fact: tan-1z = (i/2)log((i+z)/(i-z)). Then with substitutions we have (i/2)log((1+3i)/(-i-1)). Then I think the next step would be (i/2)(log(1+3i)-log(-1-i)). Do we then just proceed to solve log(1+3i) and log(-1-i)? I'm just a little confused...
12. ### U-Substitution in trig integral

##\int \frac{\csc{x}\cot{x}}{1+\csc^2{x}}dx## Let ##u = \csc{x}## then ##-du = \csc{x}\cot{x}dx## So, ##\int \frac{\csc{x}\cot{x}}{1+\csc^2{x}}dx## ##-\int \frac{1}{1+u^2}du = -\arctan{u} + C## ##-\arctan{\csc{x}} + C## This answer was wrong. The actual answer involved fully simplifying...
13. ### Worth learning complex exponential trig derivations in precalc?

This is a pedagogical /time management / bandwidth / tradeoff question, no argument that learning the complex exponential derivation is valuable, but is it a good strategy for preparing for first year Calculus? my 16YO son is taking AP precalc and AP calc next year and doing well, but struggled...
14. ### MHB 7.2.15 Int of trig in a radical

Evaluate the integral $I_4=\displaystyle\int_{-\pi}^{\pi}\sqrt{\frac{1+\cos{x}}{2}} \, dx$ ok offhand i think what is in the radical is trig identity but might be better way...
15. ### A Trick to Memorizing Trig Special Angle Values Table

When solving for x I get the angles 0, pi, pi/2 and 3pi/2. However, I thought I should reject the pi/2 and 3pi/2 values since they are not in the domain of sec^2(x). I am using the opens tax precalc book and their answer does not reject those two angles.
17. ### MHB -7.3.89 Integral with trig subst

$\begin{array}{lll} I&=\displaystyle\int{\frac{dx}{x^2\sqrt{x^2-16}}} \quad x=4\sec\theta \quad dx=4\tan \theta\sec \theta \end{array}$ just seeing if I started with the right x and dx or is there better Mahalo
18. ### Limit calculation involving log and trig functions

This was the question, The above solution is the one that I got originally by the question setters, Below are my attempts (I don't know why is the size of image automatically reduced but hope that its clear enough to understand), As you can see that both these methods give different answers...
19. ### What is the proof for the rare trig identity with tan/tan = other/other?

Came across this trig identity working another problem and I've never seen it before in my life. I don't need to prove it myself, necessarily, but I would really like to see a proof of it (my scouring of the internet has yielded no results). If someone more trigonometrically talented than myself...
20. ### MHB 8.aux.27 Simplify the trig expression

$\tiny{8.aux.27}$ Simplify the expression $\dfrac{{\cos 2x\ }}{{\cos x-{\sin x\ }\ }} =\dfrac{{{\cos}^2 x-{{\sin}^2 x\ }\ }}{{\cos x\ }-{\sin x\ }} =\dfrac{({\cos x}-{\sin x})({\cos x}+{\sin x\ })}{{\cos x}-{\sin x}} =\cos x +\sin x$ ok spent an hour just to get this and still not sure suggestions?

50. ### Finding the limit using a trig identity

Find the limit as x approaches 0 of x2/(sin2x(9x)) I thought I could break it up into: limit as x approaches 0 ((x)(x))/((sinx)(sinx)(9x)). So that I could get: limx→0x/sinx ⋅ limx→0x/sinx ⋅ limx→01/9x. I would then get 1 ⋅ 1 ⋅ 1/0. Meaning it would not exist. However the solution is 1/81...