# Relationship between sine and tangent

1. Oct 2, 2006

### x.xmedzx.x

hey guys...so my teacher gave me this lil assignment and she said to explain (in words) the relationship between sine and tangent and cosine and tangent.i have no clue what im doing...so if someone could PLEASE explain this to me...i will be so greatful!
thankz

Last edited: Oct 2, 2006
2. Oct 2, 2006

### x.xmedzx.x

sine...

hey guys...so my teacher gave me this lil assignment and she said to explain (in words) the relationship between sine and tangent and cosine and tangent.i have no clue what im doing...so if someone could PLEASE explain this to me...i will be so greatful!
thankz

3. Oct 2, 2006

### Stevedye56

what were you told in class about them? Does SOH CAH TOA mean anything of importance?

4. Oct 2, 2006

### x.xmedzx.x

no i don't think it has anything to do with that...we were looking at the graphs of sine,cosine and tangent today in class and she told us to explain the relationships...so i have so clue what she really ment

5. Oct 2, 2006

6. Oct 2, 2006

7. Oct 2, 2006

### Swapnil

I don't know how you can explain those things "in words," but I'll give it a try.

Sine, Cosine, and Tangent, are essentially defined in terms of angles and sides of a right triangle. $$\sin(\theta)$$ is a function which takes an angle of a right triangle as its input and returns the ratio of the length of the opposite side and the length of the hypotonuse. Similarly $$\cos(\theta)$$ is a function which takes an angle of a right triangle as its input and returns the ratio of the length of the adjacent side and the length of the hypotonuse. Likewise, $$\tan(\theta)$$ is a function which takes an angle of a right triangle as its input and returns the ratio of the length of the opposite side and the length of the adjacent side.

8. Oct 2, 2006

### Stevedye56

9. Oct 2, 2006

If you have a point $$P(x,y)$$ on the unit circle, then $$x = \cos \theta$$, $$y = \sin \theta$$, and $$\tan x$$ is the ratio of the y-coordinate over the x-coordinate or $$\frac{\sin \theta}{\cos \theta}$$.

10. Oct 3, 2006

### HallsofIvy

Staff Emeritus
This was also posted in the homework section. I'm merging the two threads.

11. Oct 3, 2006

### Gib Z

well, i think, seeing as you were studying the graphs, they wants you to realise the sine graph divided by cos graph equated to the tangent graph. eg they wanted you to realise the tan graph wasnt defined were cos equalled zero (division by zero impossible). and notice that the values of tan and sin were the same wen cos equalled one, etc etc.hopefully this helped.

of course this simple relation is easy to see.
sin= opposite/hypotenuse
cos= ajacent/hypotenuse

(o/h)/(a/h)= o/a

opposite/adjacent, as we well know, it the tan ratio.

12. Oct 3, 2006

### Stevedye56

Thats what I said with SOH CAH TOA

13. Oct 3, 2006

### x.xmedzx.x

o well i got it...it has to do with the the period,amplitude,max,min,domain and range.thankz for ur help everyone!