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?

  1. fraction numerator square root of 3 over denominator 2 end fraction    
  2. fraction numerator 1 over denominator 2 end fraction    
  3. fraction numerator negative 1 over denominator 2 end fraction    
  4. fraction numerator negative square root of 3 over denominator 2 end fraction    

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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