SOLUTION: The line with equation y + 2x = 0 coincides with the terminal side of an angle θ in standard position in Quadrant IV . What is the value of tan0? The line with equatio

Algebra ->  Trigonometry-basics -> SOLUTION: The line with equation y + 2x = 0 coincides with the terminal side of an angle θ in standard position in Quadrant IV . What is the value of tan0? The line with equatio      Log On


   

Question 1074693: The line with equation y + 2x = 0 coincides with the terminal side of an angle θ in standard position in Quadrant IV .
What is the value of tan0?

The line with equation −a+3b=0 coincides with the terminal side of an angle θ in standard position and sin θ<0 .
What is the value of cosθ ?





Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1) Line y%2B2x=0
Maybe your teacher instructor defined trigonometric functions
based on the coordinates of P%28x%5BP%5D%2Cy%5BP%5D%29 , with .
My 9th grade math teacher defined than%28theta%29=y%5BQ%5D .
Either way it is tan%28theta%29=y%5BR%5D%2Fx%5BR%5D for some point R%28x%5BR%5D%2Cy%5BR%5D%29
on that blue line that passes through the origin O%280%2C0%29 ,
y%2B2x=0 <---> y=-2x .
Of course that tan%28theta%29=y%5BR%5D%2Fx%5BR%5D=%28y%5BR%5D-0%29%2F%28x%5BR%5D-0%29 is the slope of the line,
and the slope of y=-2x is highlight%28-2%29%29 ,
the coefficient of x
in the slope-intercept form of the equation of the line.

1) Line -a%2B3b=0
would have to be graphed on a pait if a-b axes.
I would use the usual x-y axes and say that system+%28a=x%2Cb=y%29 .
Then, the line would be -x%2B3y=0 <--> 3y=x <--> y=%281%2F3%29x .
tan%28theta%29=1%2F3
If sin%28theta%29%3E0 ,
sin%28theta%29=sqrt%281-cos%5E2%28theta%29%29 and
since tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ,
sqrt%281-cos%5E2%28theta%29%29%2Fcos%28theta%29=1%2F3
sqrt%281-cos%5E2%28theta%29%29=cos%28theta%29%2F3
Squaring both sides,
1-cos%5E2%28theta%29=cos%5E2%28theta%29%2F9
9-9cos%5E2%28theta%29=cos%5E2%28theta%29
9=10cos%5E2%28theta%29
9%2F10=cos%5E2%28theta%29
sin%28theta%29=sqrt%281-9%2F10%29
sin%28theta%29=sqrt%281%2F10%29
and
highlight%28sin%28theta%29=sqrt%2810%29%2F10%29