Question

if sin theta = 3by5 calculate cos theta and cot theta​

Answer 1

Answer:

hope it will help u

Step-by-step explanation:

sin theta 3/5

hypt^2 = first side ^2+ another ^2

5^2= 3^2+ another side ^2

25=9+ another side^2

16= another side^2

4 = another side

cos theta = 4/5

cot theta=5/3

Answer 2

In order to solve this question, consider a simple right angled triangle in which 2 sides are 3 cm, 4 cm and the Hypotenuse is 5 cm.

Also, mark an angle θ in it.

(Refer attachment)

$\sin \theta = \dfrac{3}{5}$

$\implies \sf{ \theta = {sin}^{ - 1} \bigg( \dfrac{3}{5} \bigg) }$

$\implies \bf{ \theta = {37}^{ \circ} }$

For finding cosθ:

$\sf{cos \theta = \dfrac{adjacent \: side}{hypotenuse} }$

$\implies \boxed{ \bf{cos \theta = \dfrac{4}{5}} }$

For finding tanθ:

$\sf{tan \theta = \dfrac{sin \theta}{cos \theta} }$

$\implies \sf{tan \theta = \dfrac{3}{5} \div \dfrac{4}{5} }$

$\implies \sf{tan \theta = \dfrac{3}{5} \times \dfrac{5}{4} }$

$\implies \boxed{ \bf{tan \theta = \dfrac{3}{4} }}$

KNOW MORE:

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