alpha+beta=22/7/2 and sin alpha=1/3 then what is sin beta
so, what does 22/7/2 mean?
I think 22/7 is the approximation we used for π in the "olden days"
so a + b = π/2 or a and b are complementary angles
Construct a right angled triangles with angles a and b along with the right angle
since sina = 1/3, the missing side is √8 by Pythagoras
and sinb = √8/3 or 2√2/3
Hmph. Musta missed that. Using 22/7 for pi is just not rational!
"Using 22/7 for pi is just not rational! "
good one, they were selling t-shirts with that slogan to the math-nerds
at our University of Waterloo a few years back.
To find the value of sin(beta), we need to first find the value of beta.
Given that alpha + beta = 22/7/2 and sin(alpha) = 1/3, we can use the trigonometric identity sin(x+y) = sin(x)cos(y) + cos(x)sin(y).
In this case, let's rewrite the equation with the given values:
sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)
Now, we substitute the known values into the equation:
sin(alpha + beta) = (1/3)cos(beta) + cos(alpha)sin(beta)
Since alpha + beta = 22/7/2, we can rewrite the equation as:
sin(22/7/2) = (1/3)cos(beta) + cos(alpha)sin(beta)
To solve for sin(beta), we need to isolate it on one side of the equation.
Start by subtracting (1/3)cos(beta) from both sides:
sin(22/7/2) - (1/3)cos(beta) = cos(alpha)sin(beta)
Next, divide both sides of the equation by cos(alpha):
(sin(22/7/2) - (1/3)cos(beta)) / cos(alpha) = sin(beta)
Now, substitute the value of sin(alpha) = 1/3 into the equation:
(sin(22/7/2) - (1/3)cos(beta)) / cos(alpha) = sin(beta)
Finally, calculate the numerical value of sin(beta) using a calculator or math software with the given values of sin(alpha) = 1/3, and alpha + beta = 22/7/2.