If X and Y are in the interval (0,pie/2) and sin x =3/2 and cosy =12/13 evaluate each of the following
a)sin(x-y)
the Greek letter is pi, NOT pie!!
just use your addition formulas.
sin(x-y) = sinx*cosy - cosx*siny
Draw your triangles for x and y.
sinx = √3/2 means cosx = 1/2
cosy = 12/13 means siny = 5/13
Now just plug in the numbers.
To evaluate sin(x-y), we can use the trigonometric identity sin(A - B) = sin A * cos B - cos A * sin B.
Given sin x = 3/2 and cos y = 12/13, we need to find the values of sin y and cos x.
We can use the Pythagorean identity sin^2 A + cos^2 A = 1 to find cos x.
sin^2 x + cos^2 x = 1
(3/2)^2 + cos^2 x = 1
9/4 + cos^2 x = 1
cos^2 x = 1 - 9/4
cos^2 x = 4/4 - 9/4
cos^2 x = -5/4
Since cos x must be positive in the given interval (0, π/2), we can't find cos x from the given information. Therefore, we cannot evaluate sin(x-y) with the given information.
To evaluate sin(x-y), we need to determine the values of x and y first.
Given that sin(x) = 3/2 and x is in the interval (0, π/2), we can conclude that x is not in the range of possible values for sine. The sine function only takes values between -1 and 1. Therefore, there is no solution for sin(x) = 3/2 in the given interval.
Similarly, given that cos(y) = 12/13 and y is in the interval (0, π/2), this equation has a valid solution.
To evaluate sin(x-y), we need to know the values of both x and y. Since we only have a valid solution for y, we cannot evaluate sin(x-y) with the given information.