Solve tan(30) and tan(45)

Question

Find the distance

d = tan (30) + tan (45)

Alternative Form

d \approx - 4.785556

Calculate

tan (30), tan (45)

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

tan (30) + 0 \times i, tan (45)

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

tan (30) + 0 \times i, tan (45) + 0 \times i

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

(tan (30), 0), (tan (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 = (tan (30) - tan (45))^{2} + (0 - 0)^{2}

Solution

More Steps

Calculate

(tan (30) - tan (45))^{2} + (0 - 0)^{2}

Subtract the terms

(tan (30) - tan (45))^{2} + 0^{2}

Calculate

(tan (30) - tan (45))^{2} + 0

Add the numbers

More Steps

Evaluate

(tan (30) - tan (45))^{2} + 0

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

(tan (30) - tan (45))^{2}

Evaluate the power

tan^{2} (30) - 2 tan (30) tan (45) + tan^{2} (45)

tan^{2} (30) - 2 tan (30) tan (45) + tan^{2} (45)

Complete the square

(tan (30) + tan (45))^{2}

Reduce the index of the radical and exponent with 2

tan (30) + tan (45)

d = tan (30) + tan (45)

Alternative Form

d \approx - 4.785556

Show Solution

Midpoint = (\frac{tan ( 30 ) + tan ( 45 )}{2}, 0)

Calculate

tan (30), tan (45)

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

tan (30) + 0 \times i, tan (45)

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

tan (30) + 0 \times i, tan (45) + 0 \times i

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

(tan (30), 0), (tan (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{tan ( 30 ) + tan ( 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{tan ( 30 ) + tan ( 45 )}{2}, 0)

Show Solution