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What is the co-function of cos 37.8degrees?

I'd call it the complementary function myself because complementary angles add up to 90 degrees.

cos is short for cosine.                 co (complement of ) sine 

So   cosine(37.8) = sin(90-37.8)

 Part 1

1 mile is roughly equivalent to 1.6 km's

So   75 x 1.6 = 120 km/h.

Part 2

 1 mile is equal to 5280 feet, one hour is 3600 seconds.

So 5280/3600 = 1.4667 feet/sec.

(x-2i)(x+2i)(x-3) → (x^2 + 4)(x -3) → x^3 - 3x^2 + 4x - 12

Find the simplest polynomial with the given zeroes. 

2i, -2i, 3

a. x^3-3x^2+4x-12

b. x^3+3x^2+4x-12

c. x^3-3x^2-4x+12

d. x^3+3x^2-4x-12

\((x-2i)(x+2i)(x-3)\\ =(x^2-4i^2)(x-3) \qquad | \qquad i^2 = -1\\ =(x^2+4)(x-3)\\ =x^3-3x^2+4x-12\)

(a)

Quadrant IV

The x (real) value is positive, the y (imaginary) value is negative.

Convention in maths is to measure an angle, from the positive x-axis, in the counter-clockwise direction.

Which means that 90 degrees points up, or in the positive y-direction, 180 degrees would be pointing left (-x) and 270 degrees would be pointing down (-y).

Anywhere between 0 and 180 degrees means the vector has a positive y-component.

Anywhere between 0-90 and 270-360 degrees means the vector has a positive x-component.

In this case the vector has neither a positive x-component nor a positive y-component.

Were you to draw it, you find it points down and to the left.

So both the x and y signs are negative (-).

If your y/x ratio is negative then the signs are not equal. That means you cannot have a positive x and positive y and you cannot have both negative x and y.

The corresponding angle for positive x and y is 0-90 degrees and for negative x and y it is 180-270 degrees.

That means the possible angles are 90-180 and 270-0 degrees.

The trick here is to multiply both the numerator and the denominator with what I think is called the complex conjugate of the denominator.

In this case the conjugate is 2 - 3i. Why we do that is because when you have \((a+b)*(a-b)=(a^2-b^2)\)

Then you are left with a real denominator, because \(i^2=-1\)

Here is what I get.

\({{3+2i}\over{2+3i}}*{{2-3i}\over{2-3i}}={{6-9i+4i-6i^2}\over{4-6i+6i-9i^2}}={6-5i+6\over{4+9}}={12-5i\over{13}}\)

Simplify the following:
(3+2 i)/(2+3 i)

Multiply numerator and denominator of (3+2 i)/(2+3 i) by 2-3 i:
((3+2 i) (2-3 i))/((2+3 i) (2-3 i))

(2+3 i) (2-3 i) = 2×2+2 (-3 i)+3 i×2+3 i (-3 i) = 4-6 i+6 i+9 = 13:
((3+2 i) (2-3 i))/13

(3+2 i) (2-3 i) = 3×2+3 (-3 i)+2 i×2+2 i (-3 i) = 6-9 i+4 i+6 = 12-5 i:
Answer: |12 -  5i/13

By the ratio test, the series converges to:

sum_(n=0)^∞(2^(-n)+3^(-n)) = 7/2

First you need the definition for i which is \(i^2=-1\)

Which means that \(i=\sqrt{-1}\)

Simplify \({(2-\sqrt{-64})}+(6+\sqrt{-36})\)

This is how you can find the imaginary numbers:

\(\sqrt{-64}=\sqrt{64*-1}=\sqrt{64}*\sqrt{-1}=8*\sqrt{-1}=8i\)

You find that the first bracketed part becomes \(2-8i\)

Follow the same procedure for the second part to get your answer, the correct answer is among your options.

(1+2 i)/(log(10))

=0.43429448190325182765112891891660508229439700580366656611... +
0.86858896380650365530225783783321016458879401160733313222... i

\(\begin{array}{rll}4-\frac{x}{2}&=&\frac{x}{3}+6\\24-3x&=&2x+36\\5x&=&-12\\x&=&-\dfrac{12}{5}\end{array} \)

g(x) = x+5

f(x) = 1/x

It is likely that f(x+5) = 1/x+5

Therefore the composite function is: \((f\circ g )(x)= \dfrac{1}{x+5}\)

Pythagoras Theorem forms a relationship between the 3 sides of the triangles

\(a^2+b^2=c^2\)

Where c is the length of hypotenuse, a and b is the length of the other 2 sides.

\(60 \div 157\\\approx 0.382\)

Sorry for the messy pic I made it all by myself.

Good job anonymous 12-year-old. Me, a 13-year-old, couldn't have thought of that complex proof :O

Nope. 

cofunction of cot 37.8° would be the cofunction of tan 52.2°

60/157 = 0.38216.

Thanks Alan :D

 The cofunction of cos 37.8 degrees is sin 52.2 degrees?

I suppose if you want to really simplify the numbers then you could say that

\(\pi\approx{22\over7}\)

\(7.3\approx{51\over7}\)

\(m\approx{22\over7}*{51\over7}={{51*22}\over49}\)

Which is just over 22, because 49 is fairly close to 51.

It's not far off considering the answer is around 22.93

sin(2/3) = 0.011635265801

I just typed it into the web2 calc :)

Thanks Heureka :))