Question

find theta for which sintheta = costheta if 180°<theta<360°

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Answer 1

Answer:

The value of Theta will be 225°

Step-by-step explanation:

As per the data given in the question,

We know,

From sin graph that,

$sin225\textdegree = -\frac{1}{\sqrt{2} }$

Also, we know that, form cos graph,

$cos225\textdegree = -\frac{1}{\sqrt{2} }$

And, since 180°<225°360°

So, the value of Theta will be 225°

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Answer 2

Answer:

The value of θ lies between 180 and 225 such that the value of sinθ and cosθ is equal = 225°

Step-by-step explanation:

Given,

180°<θ<360°

sinθ = cosθ

To find,

The value of θ

Solution:

Since  θ lies between 180 and 360, hence  θ lies in the third quadrant

In the third quadrant, both sinθ and cosθ are negative

The value of sinθ  and cosθ are equal, for the value of θ = 45

Let us take, sin(180+θ) = sin (180+45) = -sin45 = -$\frac{1}{\sqrt{2} }$

cos (180+θ) = cos (180+45) = -sin 45 =  -$\frac{1}{\sqrt{2} }$

hence we have, sin 225 = cos 225 = -$\frac{1}{\sqrt{2} }$

∴The value of θ lies between 180 and 225 such that the value of sinθ and cosθ are equal = 225°

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