Question

if 2 cos 3 theta -1=0.then find the value of theta.​

Answer 1

Required Answer:-

Given:

• 2 cos(3x) - 1 = 0

To find:

• The value of x.

Solution:

Given that,

➡ 2cos(3x) - 1 = 0

➡ 2cos(3x) = 1

➡ cos(3x) = 1/2

➡ cos(3x) = 1/2

From Trigonometry Ratio Table,

➡ cos(3x) = cos(60°)

➡ 3x = 60°

➡ x = 20°

Hence, the value of x is 20°

Trigonometry Ratio Table:

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

Answer 2

Answer:

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