## anonymous one year ago FAN + MEDAL Tangent is positive in quadrants I and IV only. true or false?

1. anonymous

@Nnesha

2. Nnesha

|dw:1438291176227:dw|

3. Nnesha

remember the $$\huge\color{ReD}{\rm CAST}$$ rule

4. anonymous

?

5. anonymous

ohhhhhhhhh

6. anonymous

so false right?

7. anonymous

and SOH CAH TOA $$\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} \\ \quad \\ % tangent tan(\theta)=\cfrac{opposite}{adjacent}$$

8. anonymous

ok

9. Nnesha

yep

10. anonymous

ok thank you

11. anonymous

what about this one If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?

12. Nnesha

|dw:1438291452445:dw| remember tan = sin over cos so if sin and cos are negative tan would be positive negative divide by negative = positive

13. Nnesha

for that one you need to draw a right triangle

14. Nnesha

now they gave you the hints: cos is negative and tan is greater than 0 so at which quadrant you should draw a right triangle ?

15. anonymous

1 and 2?

16. Nnesha

no

17. Nnesha

look at the drawing in which quadrant cos is negative ?

18. anonymous

2,3,4

19. Nnesha

no that's not correct cos is negative in 2 quadrants

20. Nnesha

|dw:1438291982322:dw|

21. anonymous

ohhhhh

22. Nnesha

so cos is negative in 2nd and 3rd quadrant

23. anonymous

yup

24. anonymous

the answer is negative square root 21 over 5!!!

25. Nnesha

now given is tan>0 so as you can tan is negative in 2nd quadrant but positive in 3rd so you should draw a right triangle in 3rd quadrant|dw:1438292353952:dw| if you look at jdoe's comment *soh cah tah * rule cos = adjacent over hypotenuse now apply Pythagorean theorem to find 3rd side of right triangle

26. anonymous

ok

27. Nnesha

|dw:1438292606283:dw| sorry hypotenuse is 5 not the opposite side