## vera_ewing one year ago Math question

1. vera_ewing

2. Michele_Laino

hint: $\sin \theta = \pm \sqrt {1 - {{\left( {\cos \theta } \right)}^2}}$

3. Michele_Laino

hint: $\large \begin{gathered} \sin \theta = \pm \sqrt {1 - {{\left( {\cos \theta } \right)}^2}} = \pm \sqrt {1 - \frac{{16}}{{49}}} = \pm \sqrt {\frac{{33}}{{49}}} = ...? \hfill \\ \hfill \\ \tan \theta = \frac{{\sin \theta }}{{\cos \theta }} = \frac{{\left( { \pm \sqrt {\frac{{33}}{{49}}} } \right)}}{{ - \frac{4}{7}}} = ...? \hfill \\ \end{gathered}$

4. vera_ewing

I'm not sure...

5. Michele_Laino

hint: $\pm \sqrt {\frac{{33}}{{49}}} = \pm \frac{{\sqrt {33} }}{7}$

6. vera_ewing

@Michele_Laino Okay, so sin0 = (sqrt)33/7 ?

7. anonymous

not to butt in but this is somewhat easier if you draw a triangle

8. anonymous

|dw:1436190352602:dw|

9. anonymous

there is picture of an angle whose cosine is $$\frac{4}{7}$$ find the "opposite" side via pythagoras then you can take any trig ratio you like

10. Michele_Laino

since we have 2 square roots, then: $\sin \theta = \pm \frac{{\sqrt {33} }}{7}$

11. vera_ewing

How do we find tanθ Michele?

12. Michele_Laino

it is simple, you have to compute this ratio: $\large \tan \theta = \frac{{\sin \theta }}{{\cos \theta }} = \frac{{\left( { \pm \frac{{\sqrt {33} }}{7}} \right)}}{{ - \frac{4}{7}}} = \left( { \pm \frac{{\sqrt {33} }}{7}} \right) \times \left( { - \frac{7}{4}} \right) = ...?$

13. vera_ewing

-7(sqrt)33/28 @Michele_Laino ?

14. anonymous

|dw:1436190696248:dw|

15. anonymous

memorize the trig ratios, look at the triangle and you can find any trig ratio you like

16. anonymous

for example $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}=\pm\frac{\sqrt{33}}{7}$

17. anonymous

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=?$

18. anonymous

there is really very very little work to solve these just find the missing side of the triangle and use the trig ratios you already know

19. vera_ewing

tanθ = (sqrt)33/4 right?

20. anonymous

yes of course

21. vera_ewing

Thank you.

22. anonymous

yw