sin2(theta) cos2(theta) tan2(theta)

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nathanralph

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Aug 27, 2005
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Ok so here's the problem I have. The instructions are "Find the exact values of sin2(theta), cos2(theta), tan2(theta) for the give values of (theta).

1. cos(theta)= 3/5 0degrees < (theta) < 90degrees
2. sec(theta)=-3 90degrees < (theta) < 180degrees
3. sin(theta)=-(4/5) 270degrees < (theta) < 360degrees

Well, I can solve the problems for the most part...I just don't understand the relevancy of the second part of the question. What does it matter if theta is greater than 270, but less than 360. How does this affect it?
 
The 3 steps of data is given to help you know what quadrant you are in , ie sin of angles from 90 to 180 degrees are positve values whereas cos will be negative.
 
Ok...I understand that for the most part. However, I don't recall ever having gone over the quadrants thing where it determines which is negative and which is positive in which quadrant.

Kinda confusing...sorry.

Does anyone know this? Like, how I can put this concept to use...
 
0-90 degrees -- all postive

90-180 sin is positive, tan and cos are negative

180-270 tan is positive, sin and cos are negative

270 - 360 cos is positive, sin and tan are negative.
 
To focus in on your comment in the original posting,
What does it matter if theta is greater than 270, but less than 360. How does this affect it?

The negative result for a sin could occur from 180 - 360 degrees (2 answers are possible), however they have restricted you to the 270 -360 quadrant.

Hope that helps.
 
All right I think I've got this.

Since sin is - (4/5)

then cos is 3/5

The 4 is the negative number, because from 270-360 cos is positive.

Correct?

Or does this mean when I come up with the answer of cos2(theta) it will be positive?
 
-(4/5)

ok you are getting there...
think of a graph and plotting the points on the x&y axis. Where does the negative sign go ?

You now understand it is in the 270 - 360 quadrant, then to fit this point into this quadrant it must have a positive x value and a negative y value.

Also any positive value squared will be a positive answer, and any negative value squared = positive answer.
 
all right. So I've made this up...is this correct?

qs.jpg
 
yes the graph can then have the letters A S T C added to it to show which trig function is positive in which quadrant.

0-90 A - all
90 - 180 S - sine
180 - 270 T - tan
270 - 360 C - cos

( a student once shared with me the way they recalled the order....
ASTC -- all students talk crap)
 
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