FAN + MEDAL Tangent is positive in quadrants I and IV only. true or false?

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FAN + MEDAL Tangent is positive in quadrants I and IV only. true or false?

Mathematics
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|dw:1438291176227:dw|
remember the \(\huge\color{ReD}{\rm CAST}\) rule

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?
ohhhhhhhhh
so false right?
and SOH CAH TOA \(\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} \\ \quad \\ % tangent tan(\theta)=\cfrac{opposite}{adjacent}\)
ok
yep
ok thank you
what about this one If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?
|dw:1438291452445:dw| remember tan = sin over cos so if sin and cos are negative tan would be positive negative divide by negative = positive
for that one you need to draw a right triangle
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 ?
1 and 2?
no
look at the drawing in which quadrant cos is negative ?
2,3,4
no that's not correct cos is negative in 2 quadrants
|dw:1438291982322:dw|
ohhhhh
so cos is negative in 2nd and 3rd quadrant
yup
the answer is negative square root 21 over 5!!!
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
ok
|dw:1438292606283:dw| sorry hypotenuse is 5 not the opposite side

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