2 Answers

Eugene Burtsev · Answer 1 · 2018-06-10T21:59:54+0000

So this first wants you to find where sin is √3/2 when θ is between π and 3π/2. θ would therefore be located at 2π/3.

Now plug in the value of θ for cosine:

cos (2π/3) = -1/2

And tangent:

tan (2π/3) = -√3/3

Wujt · Answer 2 · 2018-06-15T15:23:16+0000

Answer with explanation:

Let, A=Theta

→Used the identity

Sin²A+Cos²A=1

→Sine and cosine are negative in third Quadrant.

$\sin A= (-√(3))/(2)\\\\\pi < A<(3\pi)/(2)\\\\\sin^2A+\cos^2A=1\\\\[ (-√(3))/(2)]^2+\cos^2A=1\\\\\cos^2A=1-(3)/(4)\\\\\cos^2A=(1)/(4)\\\\\cos A=\pm\ frac{1}{2}\\\\\text{As Angle lies in third Quadrant}\\\\ \cos A=(-1)/(2)\\\\\tanA=(\sinA)/(\cosA)\\\\=((-√(3))/(2))/((-1)/(2))\\\\=√(3)$

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