# Math

|(sin(x + p), sin(x + q), sin(x + r)), (sin(y + p), sin(y + q), sin(y + r)), (sin(z + p), sin(z + q), sin(z + r))|

1. 👍 0
2. 👎 0
3. 👁 104
1. Oh yeah? What is all this you have done? I don't see any work.
I get zero for the result. The full determinant value is

sin(x+p)sin(y+q)sin(z+r)+sin(y+p)sin(z+q)sin(x+r)+sin(z+p)sin(x+q)sin(y+r)
-sin(z+p)sin(y+q)sin(x+r)-sin(y+p)sin(x+q)sin(z+r)-sin(x+p)sin(z+q)sin(y+r)

Did you try using the product-to-sum formulas?

1. 👍 0
2. 👎 0
2. actually am still getting into these....i tried it but the result look scary for me plz help me sir

should i give you my email,so that you can said me the solution to study,because jishka here is a bit restricted,i seriously need help......

1. 👍 0
2. 👎 0
posted by dema
3. Recall that
sinA sinB = 1/2 (cos(A-B) - cos(A+B))
it's not too hard to expand that into
sinA sinB sinC = 1/4 (-sin(A-B-C) + sin(A+B-C) + sin(A-B+C) - sin(A+B+C))

Now, I'm afraid this little problem is just tedious algebra. At least, I don't know of a tricky identity to make things any easier. Get out a nice wide sheet of paper, and write small. You can start with

sin(x+p) sin(y+q) sin(z+r) =
1/4 (-sin(x+p-y-q-z-r) + sin(x+p+y+q-z-r) + sin(x+p-y-q+z+r) - sin(x+p+y+q+z+r))

Now you have to do that same expansion for the other five terms of the determinant. If you are careful, you will find that all those x,y,z,p,q,r expressions appear both as plus and minus terms, cancelling each other out, making the result zero.

I find very little use of such a problem assignment, as it doesn't really illustrate useful trigonometry. It's just a tricky and unexpected result.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +

asked by hayden on February 23, 2009
2. ### tigonometry

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

asked by Pablo on November 26, 2006
3. ### Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1

asked by George on September 9, 2008
4. ### Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1

asked by George on September 9, 2008
5. ### algebra

Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2

asked by Valerie on February 18, 2007
6. ### Calculus

Use a Riemann sum with n = 3 terms and the right endpoint rule to approx. ∫(1, 2) sin(1/x)dx. My teacher just needs the terms written out, no need to add or multiply. This is a problem she did up on the board, so here's her

asked by Justin on November 4, 2015
7. ### Trigonometry

Solve the equation for solutions in the interval 0

asked by Renee on March 7, 2016
8. ### Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then.

asked by George on September 8, 2008
9. ### Maths

Question : Integrate [x/(1+(sin a*sin x))] from 0 to pi My first thought was to apply integrate f(x) dx= f(a-x) dx method Which simplified the integral into; 2I = integrate [pi/(1+(sin a*sin x))] dx , cancelling out x Then I made

asked by Ashley on March 18, 2019
10. ### math

Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1

asked by Anonymous on August 3, 2007
11. ### Calculus

Hello, Could somebody kindly check my answer for the following question? Find the derivative of the following function: h(x)=3e^(sin(x+2)) h'(x)=3'(e^(sin(x+2))+3(e^(sin(x+2))' h'(x)=0(e^(sin(x+2))+3(e^(sin(x+2))(cos(1))

asked by Constantine on August 18, 2015

More Similar Questions