Trig ratios

[oliviak]

I’ve been having trouble with this question and have no idea where to start.

I know about exact ratio triangles and I assume that has something to do with it, but I’m not sure how it connects.
Thanks

 

[Harry_the_cat]

Can you draw a right angled triangle with one angle labelled theta with two appropriate sides of length 3 and 5.

 

[Deleted member 4993]

I’ve been having trouble with this question and have no idea where to start.
View attachment 34010
I know about exact ratio triangles and I assume that has something to do with it, but I’m not sure how it connects.
Thanks

Given sin(Θ) > 0 and tan(Θ) < 0 → in which quadrant/s Θ must reside?

Can you express cos(Θ) in terms of tan(Θ) ?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[oliviak]

Thats my working out so far. I've checked with the answers and it should be -5/root34, not positive. Is cos(Θ)=5/root34 negative because the angle is apparently in the second quadrant? (given by tan being negative and sin being positive)

 

[Deleted member 4993]

(given by tan being negative and sin being positive)

Yes. Another way:

sec²(Θ) = 1 + tan²(Θ) = 1 + 9/25 = 34/25

1/cos²(Θ) = 34/25 ..........→.......... cos²(Θ) = 25/34

cos(Θ) = - 5/√34 ..................negative value is chosen since Θ is in second quadrant.

 

[Steven G]

View attachment 34012
Thats my working out so far. I've checked with the answers and it should be -5/root34, not positive. Is cos(Θ)=5/root34 negative because the angle is apparently in the second quadrant? (given by tan being negative and sin being positive)

Your diagram is not correct. You need to put the triangle on the x-y plane. That is draw the x and y axes and then put your triangle in the correct quadrant. If you do that and do the same work you did above you'll get the correct answer.

 

[Harry_the_cat]

View attachment 34012
Thats my working out so far. I've checked with the answers and it should be -5/root34, not positive. Is cos(Θ)=5/root34 negative because the angle is apparently in the second quadrant? (given by tan being negative and sin being positive)

Yes that's correct. I always ignore the signs at first when I draw the triangle. Then adjust the sign according to the quadrant.

 

[Harry_the_cat]

Your diagram is not correct. You need to put the triangle on the x-y plane. That is draw the x and y axes and then put your triangle in the correct quadrant. If you do that and do the same work you did above you'll get the correct answer.

I see what you are saying, but as I replied to oliviak in previous post, I think it is ok to draw the triangle like she/he has, as long as you account for the sign later.