## anonymous one year ago The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

1. Michele_Laino

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2. anonymous

So can you explain that? lol

3. Michele_Laino

it is the representation of your problem

4. Michele_Laino

now, we can write this: $\Large OP = \sqrt {{2^2} + {3^2}} = ...$

5. Michele_Laino

what is OP?

6. Michele_Laino

I have applied the Theorem of Pitagora to the triangle OP1P

7. anonymous

the sin tan and cos?

8. Michele_Laino

yes, we have to compute OP first

9. anonymous

ok

10. Michele_Laino

hint: $\Large OP = \sqrt {{2^2} + {3^2}} = \sqrt {4 + 9} = ...?$

11. anonymous

is it just square root of 13

12. Michele_Laino

yes!

13. anonymous

14. anonymous

for all three

15. Michele_Laino

no, since we have to apply these formulas: $\Large \begin{gathered} \cos \theta = \frac{{O{P_1}}}{{OP}} = \frac{2}{{\sqrt {13} }} = ... \hfill \\ \hfill \\ \sin \theta = \frac{{P{P_1}}}{{OP}} = \frac{3}{{\sqrt {13} }} = ... \hfill \\ \end{gathered}$

16. Michele_Laino

finally, by definition, we can write: $\Large \tan \theta = \frac{{P{P_1}}}{{O{P_1}}} = ...$

17. anonymous

3/2?

18. Michele_Laino

yes!

19. anonymous

sweet thanks for the help!

20. Michele_Laino

:)