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3 years ago

If sin theta = - squrt.3/2 and pi < theta < 3pi/2, what are the values of cos theta and tan theta?

Mathematics

2 answers:

attashe74 [19]3 years ago

8 0

Answer with explanation:

Let, A=Theta

→Used the identity

Sin²A+Cos²A=1

→Sine and cosine are negative in third Quadrant.

$\sin A= \frac{-\sqrt{3}}{2}\\\\\pi < A$

Kryger [21]3 years ago

7 0

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

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The Proof for

△ABD ≅ △CBD is below

Step-by-step explanation:

Given:

$\overline{AC} \perp \overline{BD}$

$\overline{BD} \ bisects\ \overline{AC}$

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To Prove:

△ABD ≅ △CBD

Proof:

In ΔABD and ΔCBD

BD ≅ BD ....……….{Reflexive Property}

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AD ≅ CD ....……….{ $\overline{BD} \ bisects\ \overline{AC}$ }

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3 years ago