SugarRainbow 2 years ago find sec and csc when tan=3?

1. lgbasallote

if tan = 3 then that means opposite side is 3 and adjacent side is 1. make sense?

2. SugarRainbow

i think so it's one because on the unit circle the radius is one i guess? that's how i'm thinking about it

3. lgbasallote

no.. that's actually because $\tan = 3 = \frac 31 = \frac{opposite}{adjacent}$ so opposite side is 3 and adjacent side is 1

4. lgbasallote

does it make sense now?

5. SugarRainbow

yeah okay that makes more sense

6. lgbasallote

good so that means hypotenuse is $\huge \sqrt{3^2 + 1^2}\implies \sqrt{9 + 1} \implies \sqrt {10}$ right?

7. SugarRainbow

yeah that makes comeplete sense! okay so in another question i have to find tan and cot when sec=4 so does that mean....

8. lgbasallote

$\sec = 4 = \frac 41 = \frac{hypotenuse}{adjacent}$ so that means hypotenuse = 4 and adjacent = 1 right?

9. SugarRainbow

the hypotenuse is 4 and the adjacent angle is 1?|dw:1347253071421:dw|

10. lgbasallote

now....use pythagorean theorem $\huge a^2 + b^2 = c^2$ $\huge \implies a^2 = c^2 - b^2$ $\huge \implies a = \sqrt{c^2 - b^2}$ got it?

11. SugarRainbow

yeah okay i think i getting this! okay last thing, what if i get something wierd like cos=0.8?

12. lgbasallote

0.8 means 8/10

13. lgbasallote

you turn them into fractions

14. SugarRainbow

okay so whenever i get a number i think of that number over what gives me that right?

15. lgbasallote

hmm many word plays but it sounds about right

16. SugarRainbow

okay cool thank you so much!

17. lgbasallote

welcome