Solve sin(4555) and cos(45)

Question

Find the distance

d = sin (4555) + cos (45)

Alternative Form

d \approx 0.220885

Calculate

sin (4555), cos (45)

Any real number can be written as a complex number with the imaginary part 0

sin (4555) + 0 \times i, cos (45)

Any real number can be written as a complex number with the imaginary part 0

sin (4555) + 0 \times i, cos (45) + 0 \times i

The complex number for a+bi can be represented as an ordered pair (a,b)

(sin (4555), 0), (cos (45), 0)

The distance between the points (a,b) and (s,t) in the complex plane is d = (s - a)^{2} + (t - b)^{2}

d = (sin (4555) - cos (45))^{2} + (0 - 0)^{2}

Solution

More Steps

Calculate

(sin (4555) - cos (45))^{2} + (0 - 0)^{2}

Subtract the terms

(sin (4555) - cos (45))^{2} + 0^{2}

Calculate

(sin (4555) - cos (45))^{2} + 0

Add the numbers

More Steps

Evaluate

(sin (4555) - cos (45))^{2} + 0

Removing 0 doesn't change the value,so remove it from the expression

(sin (4555) - cos (45))^{2}

Evaluate the power

sin^{2} (4555) - 2 sin (4555) cos (45) + cos^{2} (45)

sin^{2} (4555) - 2 sin (4555) cos (45) + cos^{2} (45)

Complete the square

(sin (4555) + cos (45))^{2}

Reduce the index of the radical and exponent with 2

sin (4555) + cos (45)

d = sin (4555) + cos (45)

Alternative Form

d \approx 0.220885

Show Solution

Midpoint = (\frac{sin ( 4555 ) + cos ( 45 )}{2}, 0)

Calculate

sin (4555), cos (45)

Any real number can be written as a complex number with the imaginary part 0

sin (4555) + 0 \times i, cos (45)

Any real number can be written as a complex number with the imaginary part 0

sin (4555) + 0 \times i, cos (45) + 0 \times i

The complex number for a+bi can be represented as an ordered pair (a,b)

(sin (4555), 0), (cos (45), 0)

The midpoint between the points (a,b) and (s,t) in the complex plane is Midpoint= (\frac{a + s}{2}, \frac{b + t}{2})

Midpoint = (\frac{sin ( 4555 ) + cos ( 45 )}{2}, \frac{0 + 0}{2})

Solution

More Steps

Calculate

\frac{0 + 0}{2}

Removing 0 doesn't change the value,so remove it from the expression

\frac{0}{2}

Divide the terms

0

Midpoint = (\frac{sin ( 4555 ) + cos ( 45 )}{2}, 0)

Show Solution