Question

If $\sf{ Sin \; \theta }$ is 1/2 than find the value of $\sf{ 3 \; Cos \; \theta }$ $\sf{ 4 \; Tan \; \theta }$ .


Thank you :)​

Answer 1

$\sf\large\underline{\underline{\red{\sf Question:}}}$

• If sinθ is 1/2 then find the value of 3 cosθ 4tanθ .

$\sf\large\underline{\underline{\red{\sf Solution:}}}$

Steps to Solve : As per given , we have sinθ = 1/2 and we have to find the Valve of 3 cosθ 4tanθ for that firstly we have to find out the value of theta(θ) from the trigonometric table {provided below} so that we can put it in 3 cosθ 4tanθ to know our answer.

Let's start solving ,

⇒ sinθ = 1/2

⇒ sinθ = sin30°

⇒ θ= 30°

So here we got the value of theta(θ) , now we have to put the value of theta(θ) in 3 cosθ 4tanθ .

$\purple{\underbrace{\mathfrak{Substituting\: the\:value\: of \: theta(\theta)}}} :$

3 cosθ 4tanθ

⇒ 3 cos30° 4tan30°

$\sf\implies 3\left(\dfrac{\sqrt3}{2}\right)\times 4\left(\dfrac{1}{\sqrt3}\right)$

$\implies\sf\dfrac{3\sqrt3}{2}\times\dfrac{4}{\sqrt3}$

$\implies\sf\dfrac{12\;\;\cancel{\sqrt3}}{2\;\;\cancel{\sqrt3}}$

$\implies\sf\cancel{\dfrac{12}{2}}$

⇒ 6

So our answer is 6.

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$\sf\large\underline{\underline{\red{\sf Trigonometric\:table :}}}$

$\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}$