Q.1 If θ is the positive …
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Q.1 If θ is the positive acute angle , then solve the equation
4 cos2 θ - 4 sinθ = 1 .
Q.2 Find the value of sin 2θ , when tan θ = 247 and θ lies in 3rd quadrant.
Q.3 If sinθ = 1213 , then find the quadrants in which θ can lie. Also , find the values of the remaining trigonometric ratios of θ .
Q.4 A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight and describes 88m, when it has traced out 720 at the centre. Then, find the length of rope.
Posted by Abhishek Kapoor 8 years, 6 months ago
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Rashmi Bajpayee 8 years, 6 months ago
Q.2 {tex}\sin 2\theta = {{2\tan \theta } \over {1 + {{\tan }^2}\theta }}{/tex}
Since {tex}\theta {/tex} is in third quadrant, therefore value of tangent is positive.
{tex}\Rightarrow{/tex} {tex}\sin 2\theta = {{2 \times {{24} \over 7}} \over {1 + {{\left( {{{24} \over 7}} \right)}^2}}}{/tex}
{tex}\Rightarrow{/tex} {tex}\sin 2\theta = {{{{48} \over 7}} \over {1 + {{576} \over {49}}}}{/tex}
{tex}\Rightarrow{/tex} {tex}\sin 2\theta = {{48} \over 7} \times {{49} \over {625}} = {{336} \over {625}}{/tex}
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