cos ? = -4/9 with ? in quadrant II, find sin ?

Question

I don't complete get how to do this and im on a online class can you please help me?

Answer 1

Quadrant refers to a zone on a graph.

 

On your graph paper, draw the x and y axes---you can see that the paper is now divided into four sections (called "quadrants").  By convention, they are identified as follows:

I:    top-right, x and y both +

II:   top-left, x -, and y +

III:  bottom-left, x and y both -

IV:  bottom-right, x +, and y -

 

On this graph, and angle is defined by drawing a line from the origin (the crossing of the x and y axes) to a point.  the angle is measured counter-clockwise from the +x axis.

 

So:

Draw a line from the origin to the point:  x = -9, y = 4  We know this because the slope is stated as -4/9, and we are told that the line is in the 2nd quadrant.

We now see that the angle defined by this line is > 90 degrees.  This means that we have to take the cosine of the complementary angle, and then subtract that from 180.

 

X = the unknown  angle.

cos (180 - X) = 4/9

 

180 - X = arccos ( 4/9 ) = 63.6 deg.

so X = 180 - 63.6 = 116.4 deg.

 

Note that we get the same answer using:

X = arccos ( -4/9 )

 

Now that you know the angle, you can find the sine.

 

Answer 2

cosine of what degree equals -4/9 (-4/9)=-0.444...)

use a scientific calculator with arccos, use a table of values, or use the web to find an arcos calculator

using a value of -0.444444444444..., an arcos calculator gave me a value of 116.38779996º

now find the sine of this

sin(116.38779996º)=0.89580641648 (round off as needed)

this answer makes sense because sin(90º)=1 and sin(120º)=√(3)/2=0.866025 on the unit circle