# Why we use sin cos etc in sinusoidal wave?

By its very mane, a sinusoidal wave refers to a sine function. The cosine function is simply the sine function that is phase-shifted.

### Why it is named sinusoidal wave or sine wave in ac?

It's called a sine wave because the waveform can be reproduced as a graph of the sine or cosine functions sin(x) or cos (x).

### What is another word for sine wave?

Well sin, cos and tan can all be grouped into the section called sinusoidal functions, dunno if that's what you were looking for.

### Why sinusoidal functions are given so much of importance than other?

sinusoidal functions are the function of sin/cos then using this function minimise the jerk in the system

### How do you add two waves using Trigonometry?

Any single wave can be expressed in the formy = r*sin(xt + a) where x is the angle, t is the time, a is the phase (angle at start, when t = 0) r is the amplitude, and y is the vertical displacement of the wave. The function could, equally be defined in terms of the cosine function. Using identities such as sin(p +/- q) = cos(p)*sin(q) +/- sin(p)*cos(q) cos(p +/- q) = cos(p)*cos(q) -/+… Read More

### What is sinusoidal voltage wave?

A sinusoidal voltage waveform is one where the voltage as a function of time follows the trigonometric function sin(x). Frequency is typically 60Hz or 50Hz, depending on what part of the world you are in.

### Verify that sin minus cos plus 1 divided by sin plus cos subtract 1 equals sin plus 1 divided by cos?

[sin - cos + 1]/[sin + cos - 1] = [sin + 1]/cosiff [sin - cos + 1]*cos = [sin + 1]*[sin + cos - 1] iff sin*cos - cos^2 + cos = sin^2 + sin*cos - sin + sin + cos - 1 iff -cos^2 = sin^2 - 1 1 = sin^2 + cos^2, which is true,

### How do you prove this trigonometric relationship sin3A equals 3sinA cos 2 A - sin 3 A?

sin(3A) = sin(2A + A) = sin(2A)*cos(A) + cos(2A)*sin(A)= sin(A+A)*cos(A) + cos(A+A)*sin(A) = 2*sin(A)*cos(A)*cos(A) + {cos^2(A) - sin^2(A)}*sin(A) = 2*sin(A)*cos^2(A) + sin(a)*cos^2(A) - sin^3(A) = 3*sin(A)*cos^2(A) - sin^3(A)

### How would you prove left cosA plus sinA right times left cos2A plus sin2A right equals cosA plus sin3A?

You need to make use of the formulae for sin(A+B) and cos(A+B), and that cos is an even function: sin(A+B) = cos A sin B + sin A cos B cos(A+B) = cos A cos B - sin A sin B cos even fn → cos(-x) = cos(x) To prove: (cos A + sin A)(cos 2A + sin 2A) = cos A + sin 3A The steps are to work with the left hand side… Read More

### How do you show that 2 sin squared x minus 1 divided by sin x minus cos x equals sin x plus cos x?

(2 sin^2 x - 1)/(sin x - cos x) = sin x + cos x (sin^2 x + sin^2 x - 1)/(sin x - cos x) =? sin x + cos x [sin^2 x - (1 - sin^2 x)]/(sin x - cos x) =? sin x + cos x (sin^2 x - cos^2 x)/(sin x - cos x) =? sin x + cos x [(sin x - cos x)(sin x + cos x)]/(sin x… Read More

### How do you write a sinusoidal equation from a chart?

we see the amplitude of the wave and carefully note it then we see the starting from the x axis and then write the equation in sin form

### How do you simplify cos theta times csc theta divided by tan theta?

'csc' = 1/sin 'tan' = sin/cos So it must follow that (cos) (csc) / (tan) = (cos) (1/sin)/(sin/cos) = (cos) (1/sin) (cos/sin) = (cos/sin)2

### How do I find the product z1z2 if z1 5(cos20 plus isin20) and z2 8(cos15 plus isin15)?

Like normal expansion of brackets, along with: cos(A + B) = cos A cos B - sin A sin B sin(A + B) = sin A cos B + cos A sin B 5(cos 20 + i sin 20) × 8(cos 15 + i sin 15) = 5×8 × (cos 20 + i sin 20)(cos 15 + i sin 15) = 40(cos 20 cos 15 + i sin 15 cos 20 + i cos 15… Read More

### How do you simplify cos times cot plus sin?

cos*cot + sin = cos*cos/sin + sin = cos2/sin + sin = (cos2 + sin2)/sin = 1/sin = cosec

### Uses of sin cos ect in maths?

The uses of Sin, Cos etc. in Maths is in relation to Trigonometry. Trigonometry is the study of the relationship between angles and lengths of triangles.

### Factor sin cubed plus cos cubed?

sin cubed + cos cubed (sin + cos)( sin squared - sin.cos + cos squared) (sin + cos)(1 + sin.cos)

### Prove each Indentity tanx mins sinx divided by tanxsinx equals tanxsinx divided by tanx plus sinx?

(tan x - sin x)/(tan x sin x) = (tan x sin x)/(tan x + sin x) [sin x/cos x) - sin x]/[(sin x/cos x)sin x] =? [(sin x/cos x)sin x]/[sin x/cos x) + sin x] [(sin x - sin x cos x)/cos x]/(sin2 x/cos x) =? (sin2 x/cos x)/[(sin x + sin x cos x)/cos x) (sin x - sin x cos x)/sin2 x =? sin2 x/(sin x + sin x cos x) [sin… Read More

### Sin x divided by 1 minus cos x equals csc plus cot x?

It helps to convert this kind of equation into one that has only sines and cosines, by using the basic definitions of the other functions in terms of sines and cosines. sin x / (1 - cos x) = csc x + cot x sin x / (1 - cos x) = 1 / sin x + cos x / sin x Now it should be easy to do some simplifications: sin x / (1… Read More

### Verify cot x-180 cot x?

cot x = (cos x) / (sin x) cos (x - 180) = cos x cos 180 + sin x sin 180 = - cos x sin (x - 180) = sin x cos 180 - cos x sin 180 = - sin x cot (x - 180) = (cos (x - 180)) / (sin (x - 180)) = (- cos x) / (- sin x) = (cos x) / (sin x) = cot x

### How do you verify the identity of cos θ tan θ equals sin θ?

To show that (cos tan = sin) ??? Remember that tan = (sin/cos) When you substitute it for tan, cos tan = cos (sin/cos) = sin QED

### Is sin 2x equals 2 sin x cos x an identity?

Yes. sin(A+B) = sin A cos B + cos A sin B If A = B = x, this becomes: sin(x+x) = sin x cos x + cos x sin x → sin 2x = 2 sin x cos x

### How do you proof the formula sin2A equals 2sinAcosA?

First, note that sin(a+b)=sin(a)cos(b)+sin(b)cos(a) [For a proof, see: www.mathsroom.co.uk/downloads/Compound_Angle_Proof.ppt For the case of b=a, we have: sin (a+a)=sin(a)cos(a)+sin(a)cos(a) sin (2a)=2*sin(a)cos(a)

### What is the integral of sin3ycos5ydy?

Best way: Use angle addition. Sin(Ax)Cos(Bx) = (1/2) [sin[sum x] + sin[dif x]], where sum = A+B and dif = A-B To show this, Sin(Ax)Cos(Bx) = (1/2) [sin[(A+B) x] + sin[(A-B) x]] = (1/2) [(sin[Ax]Cos[Bx]+sin[Bx]cos[Ax]) + (sin[Ax]cos[-Bx]+sin[-Bx]cos[Ax])] Using the facts that cos[-k] = cos[k] and sin[-k] = -sin[k], we have: (1/2) [(sin[Ax]Cos[Bx]+sin[Bx]cos[Ax]) + (sin[Ax]cos[-Bx]+sin[-Bx]cos[Ax])] (1/2) [(sin[Ax]Cos[Bx]+sin[Bx]cos[Ax]) + (sin[Ax]cos[Bx]-sin[Bx]cos[Ax])] (1/2) 2sin[Ax]Cos[Bx] sin[Ax]Cos[Bx] So, Int[Sin(3y)Cos(5y)dy] = (1/2)Int[Sin(8y)-Sin(2y)dy] = (-1/16) Cos[8y] +1/4 Cos[2y] + C You would get… Read More

### What does cosx divided by 1-sinx equal?

cos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x) = cos x (1 + sin x) / (1 - sin2x) = cos x (1 + sin x) / cos2 x = (1 + sin x) / cos x = sec x + tan x cos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 +… Read More

### How do you solve sinx divided by 1 plus cosx plus cosx divided by sinx?

sin x/(1+cos x) + cos x / sin x Multiply by sin x (1+cos x) =[(sin^2 x + cos x(1+cos x) ] / sin x (1+cos x) = [(sin^2 x + cos x + cos^2 x) ] / sin x (1+cos x) sin^2 x + cos^2 x = 1 = (1+cos x) / sin x (1+cos x) = 1/sin x

### How tan9-tan27-tan63 tan81 equals 4?

tan(9) + tan(81) = sin(9)/cos(9) + sin(81)/cos(81)= {sin(9)*cos(81) + sin(81)*cos(9)} / {cos(9)*cos(81)} = 1/2*{sin(-72) + sin(90)} + 1/2*{sin(72) + sin(90)} / 1/2*{cos(-72) + cos(90)} = 1/2*{sin(-72) + 1 + sin(72) + 1} / 1/2*{cos(-72) + 0} = 2/cos(72) since sin(-72) = -sin(72), and cos(-72) = cos(72) . . . . . (A) Also tan(27) + tan(63) = sin(27)/cos(27) + sin(63)/cos(63) = {sin(27)*cos(63) + sin(63)*cos(27)} / {cos(27)*cos(63)} = 1/2*{sin(-36) + sin(90)} + 1/2*{sin(72) + sin(36)} /… Read More

### How do you prove that 2 sin 3x divided by sin x plus 2 cos 3x divided by cos x equals 8 cos 2x?

You need to know the trigonometric formulae for sin and cos of compound angles. sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y) and cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) Using these, y = x implies that sin(2x) = sin(x+x) = 2*sin(x)cos(x) and cos(2x) = cos(x+x) = cos^2(x) - sin^2(x) Next, the triple angle formulae are: sin(3x) = sin(2x + x) = 3*sin(x) - 4*sin^3(x) and cos(3x) = 4*cos^3(x) - 3*cos(x) Then the left hand side = 2*[3*sin(x) - 4*sin^3(x)]/sin(x) + 2*[4*cos^3(x)… Read More

### What is this expression as the cosine of an angle cos30cos55 plus sin30sin55?

cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25) Note: cos(a)=cos(-a) for any angle 'a'. cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.

### Why sin integral is cos?

sin integral is -cos This is so because the derivative of cos x = -sin x

### Use trigonometric identities to write each expression in terms of a single trigonometric function or a constant. simplify cos t sin t?

Thanks to the pre-existing addition and subtraction theorums, we can establish the identity: sin(a+b) = sin(a)cos(b)+sin(a)cos(b) Then, solving this, we get sin(a+b) = 2(sin(a)cos(b)) sin(a)cos(b) = sin(a+b)/2 a=b, so sin(a)cos(a) = sin(a+a)/2 sin(a)cos(a) = sin(2a)/2 Therefore, the answer is sin(2a)/2.

### What is the integral of 1 divided by sin x plus cos x?

The question is ambiguous: does it refer to 1/sin(x) + cos(x) or to 1/[sin(x)+cos(x)]?

### How do you solve double angle equations for trigonometry?

There are two ways to solve for the double angle formulas in trigonometry. The first is to use the angle addition formulas for sine and cosine. * sin(a + b) = sin(a)cos(b) + cos(a)sin(b) * cos(a + b) = cos(a)cos(b) - sin(a)sin(b) if a = b, then * sin(2a) = sin(a)cos(a) + cos(a)sin(a) = 2sin(a)cos(a) * cos(2a) = cos2(a) - sin2(b) The cooler way to solve for the double angle formulas is to use Euler's… Read More

### What are five trigonometric identities?

All others can be derived from these and a little calculus: sin2x+cos2x=1 sec2x-tan2x=1 sin(a+b)=sin(a)cos(b)+sin(b)sin(a) cos(a+b)=cos(a)cos(b)-sin(a)sin(b) eix=cos(x)+i*sin(x)

### What is the solution to sec plus tan equals cos over 1 plus sin?

sec + tan = cos /(1 + sin) sec and tan are defined so cos is non-zero. 1/cos + sin/cos = cos/(1 + sin) (1 + sin)/cos = cos/(1 + sin) cross-multiplying, (1 + sin)2 = cos2 (1 + sin)2 = 1 - sin2 1 + 2sin + sin2 = 1 - sin2 2sin2 + 2sin = 0 sin2 + sin = 0 sin(sin + 1) = 0 so sin = 0 or sin =… Read More

### How can you prove that 1-2 cosine squared over sine times cosine is equal to tangent minus cotangent?

sin2 + cos2 = 1 So, (1 - 2*cos2)/(sin*cos) = (sin2 + cos2 - 2*cos2)/(sin*cos) = (sin2 - cos2)/(sin*cos) = sin2/(sin*cos) - cos2/(sin*cos) = sin/cos - cos-sin = tan - cot

### How do you convert sin to cos and other functions Please give example?

Sin = 1 / cos. And cos = 1 / -sin

### How do you simplify tan theta cos theta?

Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).

### What is tan squared theta minus sec squared theta simplified?

tan θ = sin θ / cos θ sec θ = 1 / cos θ sin ² θ + cos² θ = 1 → sin² θ - 1 = - cos² θ → tan² θ - sec² θ = (sin θ / cos θ)² - (1 / cos θ)² = sin² θ / cos² θ - 1 / cos² θ = (sin² θ - 1) / cos² θ = - cos² θ / cos² θ… Read More

### Solution for tan x plus cot x divided by sec x csc x?

(tan x + cot x)/sec x . csc x The key to solve this question is to turn tan x, cot x, sec x, csc x into the simpler form. Remember that tan x = sin x / cos x, cot x = 1/tan x, sec x = 1/cos x, csc x = 1/sin x The solution is: [(sin x / cos x)+(cos x / sin x)] / (1/cos x . 1/sin x) [(sin x… Read More

### If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?

There is a hint to how to solve this in what is required to be shown: a and b are both squared. If a cos θ + b sin θ = 8 a sin θ - b cos θ = 5 then square both sides of each to get: a² cos² θ + 2ab cos θ sin θ + b² sin² θ = 64 a² sin² θ - 2ab sin θ cos θ + b²… Read More

### Simplify sinx cotx cosx?

== cot(x)== 1/tan(x) = cos(x)/sin(x) Now substitute cos(x)/sin(x) into the expression, in place of cot(x) So now: sin(x) cot(x) cos(x) = sin(x) cos(x) (cos(x)/sin(x) ) sin(x) cos(x) cos(x)/sin(x) The two sin(x) cancel, leaving you with cos(x) cos(x) Which is the same as cos2(x) So: sin(x) cot(x) cos(x) = cos2(x) ===

### Why is sine 30 the same as cosine of 60?

sin(30) = sin(90 - 60) = sin(90)*cos(60) - cos(90)*sin(60) = 1*cos(60) - 0*sin(60) = cos(60).

### Simplyfy cos x cot x plus tan x equals?

To simplify this sort of things, it helps if, first of all, you convert everything to sines and cosines. cos x cot x + tan x (original equation) = cos (cos x / sin x) + (sin x / cos x) (convert to sin and cos) = cos2x / sin x + sin x / cos x (multiplying in the first term) = (sin x cos2x + sin x cos x) / sin x cos… Read More

### What is the 87th derivative of sin x?

The 1st derivative of the sin is cos; the 2nd is -sin; 3rd is -cos; 4th is sin; then repeats every fourth time. So 84 th is the sin; 85th cos; 86th -sin; and 87th derivative is -cos

### Why does the derivative of sin x equal - cos x?

It isn't. The derivate of sin x = cos x. It isn't. The derivate of sin x = cos x. It isn't. The derivate of sin x = cos x. It isn't. The derivate of sin x = cos x.

### How do you use the Euler's formula to obtain the sin3X in terms of cosX and sinX?

Using Euler's Formula, you use (cos(x) + i sin(x))^n = cos (nx) + i sin(nx) Now you let n=3 (cos(x) + i sin (x))3 = cos(3x) + i sin (3x) (cos(x))3 + 3(cos(x))2 * i sin(x) + 3cos(x) * i2 (sin(x))3 = cos(3x)+ i sin(3x) (cos(x))3 + i(3sin(x)(cos (x))2) - 3cos(x)(sin(x)2) - i(sin(x))3 = cos (3x) + i sin(3x) Now only use the terms with i in them to figure out what sin(3x) is... 3sin(x)(cos(x))2… Read More

### What is the derivative of cos x sin x divided by cos x sin x?

(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.

### How do you factor sin squared times x plus cos2x -cosx equals 0?

What do you mean sin squared times x? sin ^2 x means one and only one thing, (sin x) ^2 same as sin ^ n x = (sin x) ^n and cos ^n x = (cos x)^n you need to know (and why): sin ^2 x + cos ^2 x = 1 cos 2x = 1 - 2sin ^2 x (= cos ^2 x - sin ^2 x) so sin ^2 x + cos (2x)… Read More

### How do you solve the following identity sec x - cos x equals sin x tan x?

sec x - cos x = (sin x)(tan x) 1/cos x - cos x = Cofunction Identity, sec x = 1/cos x. (1-cos^2 x)/cos x = Subtract the fractions. (sin^2 x)/cos x = Pythagorean Identity, 1-cos^2 x = sin^2 x. sin x (sin x)/(cos x) = Factor out sin x. (sin x)(tan x) = (sin x)(tan x) Cofunction Identity, (sin x)/(cos x) = tan x.

### What is the solution to cos equals sec-sintan?

I'm not really sure what you mean by "the solution", but that equation cos = sec - sintan does simplify down to sin^2 + cos^2 = 1 which so happens to be an identity. I'm not sure if that's what you're looking for, but if it is, here are the steps in simplifying it. 1. Convert sec to 1/cos 2. Convert tan into sin/cos and multiply it by sin sintan = sin(sin/cos) = (sin^2)/cos You… Read More