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audioaxes

08-12-2002, 11:40 PM

2)sin2x - sinx = 0

3)sec^2(x) - 4 = 0

4)The line y = -4x + 5 makes an angle of inclination of _______ degrees with the x axis

5)the lines y = 2x - 7 and y = 3x + 5 make an angle of ______ degrees

6)the integers are the set: {_________________} ?????

ericlin

08-13-2002, 06:07 AM

sin2x - sinx = 0

solve:

x=60+120*k or 360*k;

unit is in degrees;

k is any integer;

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sec^2(x) - 4 = 0

What does this mean ?

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The line y = -4x + 5 makes an angle of inclination of _______ degrees with the x axis

solve:

make x1=0 and x2=1; Then you got y1 and y2;

The angle is (180/Math.PI)*Math.atan2(y2-y1,x2-x1);

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the lines y = 2x - 7 and y = 3x + 5 make an angle of ______ degrees

solve:

Use above calculation, then substract these two angles.

-------------------------------

the integers are the set: {_________________} ?????

??????????

audioaxes

08-13-2002, 12:34 PM

thanks;

i found out sec^2(x)=0 on my own(if its correct)

x=60 or 300 degrees

i didnt understand how you did the angle problems but i figured out a way to do it:

The line y = -4x + 5 makes an angle of inclination of _______ degrees with the x axis

forms a triangle: 5=long leg(y intercept) then you find the x intercept for the short leg(1.25) i did tan to find the angle= 75.9 but i dont know what an angle of inclination is: is it this angle or is it the other angle(104.1) made by the line with the x axis

audioaxes

08-13-2002, 12:53 PM

but i havent found out how to do the problem: <i>5)the lines y = 2x - 7 and y = 3x + 5 make an angle of ______ degrees</i>

<b>make x1=0 and x2=1; Then you got y1 and y2;

The angle is (180/Math.PI)*Math.atan2(y2-y1,x2-x1);

Use above calculation, then substract these two angles</b>

-i didnt understand this

ericlin

08-13-2002, 01:34 PM

Try imagine your triangle as rectangle and put focus on the other triangle in this rectangle, you will get the inclination angle.

The short leg will be 1.25 and the long leg will be -5;(different now). Than you can calculate the tan for angle;

In fact, y=-4x+5; only the slope (-4) decides the inclination angle. (+5) does not matter.

So, in my equation, when x=0, y will be 5; when x=1;y will be 1; We get two points (0,5) and (1,1); It is also a small triangle; The tan of this angle is the slope (y2-y1)/(x2-x1); that is -4; So the angle is -76 degrees;

To get the cross angle of y = 2x - 7 and y = 3x + 5;

The first line inclination angle to the x axis is

(180/Math.PI)*Math.atan2(2,1); slope=2;

The result is 71.5 degrees;

For the second line, slopw is 3; The x-axis inclination is:

(180/Math.PI)*Math.atan2(3,1);

The result is 63.4 degrees;

So the cross angle is angleA-angleB;

71.5-63.4=8.1 degrees;

Of-course, the answer can be -8.1 degree;

muckyMuckMan

08-16-2002, 07:38 PM

sec^2(x) - 4 = 0

Use the secant/tangent Pythagorean identity:

(sec x)^2 = (tan x)^2 + 1

So,

[(tan x)^2 + 1] - 4 = 0

(tan x)^2 - 3 = 0

(tan x)^2 = 3

sqrt(tan^2(x)) = +/-sqrt(3)

tan x = +/- sqrt(3)

x = 60°, 120°, 240°, 300°

(I only solved for degrees in the interval 0<=x<=360)