The angle between the complex numbers 2+2i and -7

Consider the right triangle formed by the complex number in the Argand-Gauss plane and it's projections on the axis. – José Siqueira Nov 12 '13 at 17:21

In particular what is the definition of sine of theta in terms of the known sides of the above mentioned right triangle? – Adam Nov 12 '13 at 17:27

Add a comment

3 Answers

1

Consider the following Argand-diagram

enter image description here

The y-axis is the imaginary axis and the x-axis is the real one. The complex number in question is

x+yi

To figure out θ, consider the right-triangle formed by the two-coordinates on the plane (illustrated in red). Let θ be the angle formed with the real axis.

tanθ=yx

⟹tan−1(yx)

The hypotenuse of the triangle will be

x2+y2−−−−−−√

Therefore,

Step-by-step explanation:

could

step-by-step explanation:

u send me a picture of ur work

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~