Question

Given sin theta = 2/5 and 0 theta 90 find sin 2 theta

Answer 1

Answer:

The value of $\sin^2 \theta=\frac{4}{25}$                                                                            

Step-by-step explanation:

Given : $\sin \thet=\frac{2}{5}$ and  $0$

To find : The value of $\sin^2\theta$ ?

Solution :

We have given the value of $\sin \thet=\frac{2}{5}$ and  $0$

To find $\sin^2\theta$ we just have to square $\sin\theta$

$\sin \theta=\frac{2}{5}$

Squaring both sides,

$(\sin \theta)^2=(\frac{2}{5})^2$

$\sin^2 \theta=\frac{4}{25}$

Therefore, The value of $\sin^2 \theta=\frac{4}{25}$

Answer 2

Given:  sin theta = 2/5.  This tells us that the lengths of the opp side and the hyp are 2 and 5 respectively.  The adj side is found using the Pyth. Thm.:  5^2-2^2= 25-4 = 21, so that the adj side is sqrt(21).

The double angle formula for the sine is sin 2theta = 2 sin theta *cos theta.

In this particular problem, the sine of 2theta is 2*(2/5)*[sqrt(21) / 5], or:

                                                                              (4/25)*sqrt(21).