Question

How do you find sin A and tan A if cosA equals 4/5 and cot A >0.

Answer 1

cosA=4/5 corresponds to a right angled triangle with one side=4 and hypotenuse=5
From Pythagoras you then can tell the third side, which is 3.
so
\[\sin A=\frac{3}{5}\] and \[\tan A = \frac{3}{4}\]

Answer 2

Because we know that cotA>0 we also know that sinA cannot be negative (while cosA is given to be positive), so we have excluded the possibility that sinA=-3/5
(which otherwise could have been a possible solution, too)

Answer 3

Does it make sense?

Answer 4

i dont understand how you know if it is positive or negative like the cot A >0 confuses me

Answer 5

you must be able to draw a circle first :DDD

Answer 6

ok. let's look at the definition of cot:\[\cot A = \frac{\sin A}{\cos A} > 0 \]
This can be true only if either \[\sin A > 0, \cos A>0\] or \[\sin A <0, \cos A <0\]
agree?

Answer 7

Once you agree with that you can exclude the second possibility, since we're told that cosA=4/5 > 0 --> so sinA cannot be < 0.

Answer 8

sorry i correct myself cot should be \[\cot A=\frac{\cos A}{\sin A}\] but the argument is the same...