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Maths-

General

Easy

Question

In the given figure, θ is an angle. If $s i n invisible function application theta equals fraction numerator square root of 3 over denominator 2 end fraction$ , what is cos θ?

$\frac{\sqrt{3}}{2}$
$\frac{1}{2}$
$\frac{- 1}{2}$
$\frac{- \sqrt{3}}{2}$

The correct answer is: $fraction numerator negative 1 over denominator 2 end fraction$

$s i n to the power of 2 end exponent invisible function application theta plus C o s to the power of 2 end exponent invisible function application theta equals 1$
Step-by-step solution:-
From the above formula-
$Sin to the power of 2 end exponent invisible function application theta plus Cos to the power of 2 end exponent invisible function application theta equals 1$
$fraction numerator left parenthesis square root of 3 right parenthesis to the power of 2 end exponent over denominator left parenthesis 2 right parenthesis to the power of 2 end exponent end fraction plus c o s to the power of 2 end exponent invisible function application theta equals 1$
∴ $fraction numerator 3 over denominator 4 end fraction plus C o s to the power of 2 end exponent invisible function application theta equals 1$
$therefore C o s to the power of 2 end exponent blank theta equals 1 minus fraction numerator 3 over denominator 4 end fraction$
$therefore blank C o s 2 blank theta blank equals fraction numerator 4 minus 3 over denominator 4 end fraction$
∴ $c o s to the power of 2 end exponent invisible function application theta equals fraction numerator 1 over denominator 4 end fraction$
$therefore C o s invisible function application theta equals plus divided by negative fraction numerator 1 over denominator 2 end fraction$
Since the given angle lies in the second quadrant and the sign of Cos θ in the second quadrant is always negative,
∴ Cos θ = $fraction numerator negative 1 over denominator 2 end fraction$
Final Answer:-
Option C i.e. $fraction numerator negative 1 over denominator 2 end fraction$ is the correct Option.

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