11.12.2015

The sine values

The unit circle can be considered not only for individual trigonometric functions, but also under the microscope each function separately. Here are the sine values for different angles.

sin 0. Mathematics for blondes.
sin 0

sin 30. sin p/6, sine 1/6 pi. Mathematics for blondes.
sin 30
sin 45, sin p/4, sine pi/4. Mathematics for blondes.
sin 45
sin 60, sine p/3, sin pi/3. Mathematics for blondes.
sin 60
sin 90, sin p/2, sin pi/2, sine 1/2 pi. Mathematics for blondes.
sin 90
sin 120, sin 2p/3, sin 2pi/3, sine 2/3 pi. Mathematics for blondes.
sin 120
sin 135 degrees, sin 3p/4, sin 3pi/4, sine 3/4 pi radians. Mathematics for blondes.
sin 135
sin 150, sine 5/6 pi radians, sin 5p/6, sin 5 pi by 6. Mathematics for blondes.
sin 150
sin 180, sin pi. Mathematics for blondes.
sin 180
sin 210, sin 7p/6, sin 7/6 pi. Mathematics for blondes.
sin 210
sin 225, sin 5/4 pi, sin 5p/4. Mathematics for blondes.
sin 225
sin 240, sin 4p/3, sine 4 pi division by 3 radians, sin 4/3 pi. Mathematics for blondes.
sin 240
sin 270, sin 3pi/2, sine 3/2 pi. Mathematics for blondes.
sin 270
sin 300, sin 5p/3, sin 5/3 pi. Mathematics for blondes.
sin 300
sin 315, sin 7pi/4, sin 7/4 pi. Mathematics for blondes.
sin 315
sin 330, sin 11pi/6, sin 11/6 pi. Mathematics for blondes.
sin 330
sin 360, sin 2pi, sine 2 pi radians. Mathematics for blondes.
sin 360

The unit circle is like a movie that shows us mathematics. Here you see some pictures of the cult TV series.

11.11.2015

Unit circle

Mathematicians consider themselves clever and all the rest. But not all of us are as smart as mathematics. The unit circle mathematics invented for themselves. For those who are just beginning to study mathematics, I suggest a simpler version - separately cosines and sines separately.

If we remove from the unit circle all that relates to the sine, we get the unit circle cosines.

Unit circle cosines. Cos 0, cos 30, cos 45, cos 60, cos 90. Mathematics for blondes.
Unit circle cosines

If we remove from the unit circle everything about cosines, we get a unit circle sinuses.

Unit circle sinuses. Sin 0, sin 30, sin 45, sin 60, sin 90. Mathematics for blondes.
Unit circle sinuses

Now, you will not confuse the values of sines and cosines.

11.10.2015

Degrees, minutes, seconds

I was write: "Help me to understand. It is necessary to determine how many degrees, minutes, and seconds contains 4563 seconds corner. Only by actions, and I completely confused."

No harly-barly! We sit quietly and remember that one minute contains 60 seconds, in one degree contains 60 minutes. Now we pimenyaem our knowledge into practice. Transform seconds in a minutes.

4563 : 60 = 76.05 minutes

Determine how many seconds we leave intact:

4563 - 60 * 76 = 4563 - 4560 = 3 seconds

Now 76 minutes translate into degrees, still sadly dividing by 60:

76 : 60 = 1.26667 degrees

We calculate how many minutes do not fit into the clothes degrees:

76 - 60 * 1 = 76 - 60 = 16 minutes

Now our suffering ended and we in good conscience can write the final result:

4563 seconds = 1 degree 16 minutes 3 seconds

Checking? We translate everything back to the second:

1 * 60 * 60 + 16 * 60 + 3 = 3600 + 960 + 3 = 4563

As the math, the conversion is correct.