cos a= -3/4, a= [p,3p/2] найти sin a tg a ctg a

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Given that a = -3/4 and a is in the interval [p, 3p/2], let's find sin(a), tan(a), and cot(a).

First, let's find the reference angle for 'a' within the given interval [p, 3p/2].

a = -3/4
To find the reference angle, we add 2π to a in order to get it in the desired interval:

a = -3/4 + 2π
a = 5π/4

Now, we will find sin(a), tan(a), and cot(a).

sin(a) = sin(5π/4)
sin(5π/4) = -√2 / 2

tan(a) = tan(5π/4)
tan(5π/4) = sin(5π/4) / cos(5π/4)
tan(5π/4) = -√2 / 2 / (-1 / √2)
tan(5π/4) = √2

cot(a) = 1 / tan(5π/4)
cot(5π/4) = 1 / √2

Therefore, sin(a) = -√2 / 2, tan(a) = √2, and cot(a) = 1 / √2.