Question

If root 3sintheta-costheta=0 and 0° <theta< 90, find the value of theta
​

Answer 1

Required Answer:-

Given:

• √3 sin(θ) - cos(θ) = 0
• 0° < θ < 90°

To find:

• The value of θ

Solution:

Given that,

➡ √3 sin(θ) - cos(θ) = 0

➡ √3 sin(θ) = cos(θ)

➡ sin(θ)/cos(θ) = 1/√3

➡ tan(θ) = 1/√3

From Trigonometry Ratio Table,

➡ tan(θ) = tan(30°)

➡ θ = 30°

Hence, the value of θ is 30°

Answer:

• θ = 30°

Trigonometry Ratio Table:

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

Relationship between Trigonometric Functions:

• sin(θ) = 1/cosec(θ)
• cos(θ) = 1/sec(θ)
• tan(θ) = 1/cot(θ)
• sin(θ)/cos(θ) = tan(θ)