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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 the same result if you used integration by parts twice and played around with trig identities.
How do you prove sin x tan x equals cos x?
You can't. tan x = sin x/cos x So sin x tan x = sin x (sin x/cos x) = sin^2 x/cos x.
What is sine squared?
Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
What is the 87th derivative of sin x?
Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x
Sin x Tan x equals Sin x?
No. Tan(x)=Sin(x)/Cos(x) Sin(x)Tan(x)=Sin2(x)/Cos(x) Cos(x)Tan(x)=Sin(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).
What is the sin 60?
sin 60 = √(3)/2 or about 0.866 ■
The shorter leg of a 30-60-90 degree triangle is 6 what is the length of the other leg?
Use the Sine rule. If L is the length of the longer leg, then L/sin(60) = 6/sin(30) So that L = 6*sin(60)/sin(30) = 12*sin(60) = 12*sqrt(3)/2 = 10.39 units.
What are the ratios of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?
The longer leg is opposite the 60 deg angle. Suppose A = 60 deg, C = 90 deg and a and c are the corresponding sides. Then, by the sine rule a/c = sin(A)/sin(C) a/c = sin(60)/sin(90) = sqrt(3)/2
How will the value of sin 35 determine?
to find sin 35 here we take the angle = x=15 then 3x=45 , 4x=60 then 4x-3x=60-45 then by putting sin on rhs we will get cos 35 and sin 35 hope it helped you
What is the cofunction of sin 30 degree?
cos 60
Find the value of sin 300 degrees?
sin 300 = -sin 60 = -sqrt(3)/2 you can get this because using the unit circle.
A hypotenuse of a 30-60-90 triangle has a length of 13 what is the length is the side opposite of the 60 degree angle?
Use trigonometry and the sine ratio: sin = opp/hyp and when rearrange hyp*sin = opp 13*sin(60) = 11.25833025 or 11.26 units in length to 2 d.p.
What is the length of the side opposite the 60 angle if the hypotenuse is 17?
The length of the side opposite the 60° angle is about 14.72(sin 60°) = 0.866The length of the side opposite the 30° angle is 8.5(sin 30°) = 0.5
Solve sin x square root of 3 by 2?
Do you mean sin(x)=sqrt(3)/2? IF so, look at at 30/60/90 triangle. We see the sin 60 degrees is square (root of 3)/2
What is exact value sin480degrees?
sin 480° is equal to sin 60°, which is sqrt(3)/2 or approximately 0.866.
What are the lengths of the missing sides of a 30-60-90 triangle if the longer leg of the triangle is 18 centimeter?
The longest side of the triangle will always be opposite the largest angle, which is 90° in this case. We can use the sine law to work out the other sides with that: sin(90°) / 18 = sin(60°) / x = sin(30°) / y 1/18 = sin(60°) / x x = 18 sin(60°) x = 18√3 / 2 x = 9√3 1/18 = sin(30°) / y y = 18 sin(30°) y = 9 So the triangle has a sides of 9 and 9√3, with a hypotenuse of 18
