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If working in radians, the cosine of one-quarter of pi is equal to the square root of 0.5. Squaring this gives 0.5, or exactly one-half.
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What is the sin pi over 4?
sin(pi/4) and cos(pi/4) are both the same. They both equal (√2)/2≈0.7071■
What is the pi r squared of a radius of 4?
Area of a circle in square units = pi*radius2
What is 4 pi r squared?
It is the formula for finding the surface area of a sphere which is 4*pi*radius2
In a circle a 90 degrees sector has an area of 225 pie in squared What is the radius of the circle?
area = 225 pi = pi R squared/4 R = square root 900 = 30 in
What is Tan pi over 4?
tangent of pi/4 = 1
What is the exact value of the expression cos 7pi over 12 cos pi over 6 -sin 7pi over 12 sin pi over 6?
cos(a)cos(b)-sin(a)sin(b)=cos(a+b) a=7pi/12 and b=pi/6 a+b = 7pi/12 + pi/6 = 7pi/12 + 2pi/12 = 9pi/12 We want to find cos(9pi/12) cos(9pi/12) = cos(3pi/4) cos(3pi/4)= cos(pi-pi/4) cos(pi)cos(pi/4)-sin(pi)sin(pi/4) cos(pi)=-1 sin(pi)=0 cos(pi/4) = √2/2 sin(pi/4) =√2/2 cos(pi)cos(pi/4)-sin(pi)sin(pi/4) = - cos(pi/4) = -√2/2
What is the exact value using a sum or difference formula of the expression cos 11pi over 12?
11pi/12 = pi - pi/12 cos(11pi/12) = cos(pi - pi/12) cos(a-b) = cos(a)cos(b)+sin(a)sin(b) cos(pi -pi/12) = cos(pi)cos(pi/12) + sin(pi)sin(pi/12) sin(pi)=0 cos(pi)=-1 Therefore, cos(pi -pi/12) = -cos(pi/12) pi/12=pi/3 -pi/4 cos(pi/12) = cos(pi/3 - pi/4) = cos(pi/3)cos(pi/4)+sin(pi/3) sin(pi/4) cos(pi/3)=1/2 sin(pi/3)=sqrt(3)/2 cos(pi/4)= sqrt(2)/2 sin(pi/4) = sqrt(2)/2 cos(pi/3)cos(pi/4)+sin(pi/3) sin(pi/4) = (1/2)(sqrt(2)/2 ) + (sqrt(3)/2)( sqrt(2)/2) = sqrt(2)/4 + sqrt(6) /4 = [sqrt(2)+sqrt(6)] /4 Therefore, cos(pi/12) = (sqrt(2)+sqrt(6))/4 -cos(pi/12) = -(sqrt(2)+sqrt(6))/4 cos(11pi/12) = -(sqrt(2)+sqrt(6))/4
What is the sin pi over 4?
sin(pi/4) and cos(pi/4) are both the same. They both equal (√2)/2≈0.7071■
How was it determined that the tangent of pi divided by 4 is 1?
As tan(x)=sin(x)/cos(x) and sin(pi/4) = cos(pi/4) (= sqrt(2)/2) then tan(pi/4) = 1
What is the value of cos pie4?
cos pi over four equals the square root of 2 over 2 This value can be found by looking at a unit circle. Cos indicates it is the x value of the point pi/4 which is (square root 2 over 2, square root 2 over 2)
What is the diameter of the circle that has a circumference equal to its area?
The diameter is 4 and its radius is 2 because 2+2 = 4 and 2 squared = 4 Circumference of the circle: pi*4 is the same as pi*2 squared Area of the circle: pi*2 squared
What are the distinct fourth root of -1?
The four roots are cos(theta)+i*sin(theta) where theta = pi/4, 3*pi/4, 5*pi/4 and 7*pi/4.
What is the diameter of a circle is the area is 400pie?
area = pi x diameter squared/4 = 400 pi diameter squared = 4 x 400 x pi/pi = 1600 diameter = sqrt 1600 = 40
What is 4 times pi times the radius squared is the surface area of a sphere?
That is correct because the surface area of a sphere is: 4*pi*radius squared
What is the side length of an 8 inch diameter octagon?
The side length is 2/[cos(pi/4)*cos(pi/8)] = 3.06 inches, approx.
What are the exact values of the sine and cosine functions of 2pi over 65537?
sin(2*pi/65537) = 0.0001 cos(2*pi/65537) = 1.0000 to 4 dp.
What is the surface area of a cylinder with 4m in diameter and 6m in height?
The surface area of a (closed) cylinder equals the surface area of both bases (the top and bottom), i.e. pi x radius squared (first base) + pi x radius squared (second base), plus the lateral surface area (the surface area of the curved side), i.e. circumference (pi x diameter) x height. Inserting the numbers: SA = pi x (2 m.) squared + pi x (2 m.) squared + pi x 4 m. x 6 m. = pi x 4 m. squared + pi x 4 m. squared + pi x 24 m. squared = 8 x pi m. squared + 24 x pi m. squared = 32 x pi meters squared.
