Question

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

Answer 1

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).

Answer 2

The value of
`\sin^2 \theta=(4)/(25)`

Explanation:

Given :
`\sin \thet=(2)/(5)` and
`0<\theta<90`

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

Solution :

We have given the value of
`\sin \thet=(2)/(5)` and
`0<\theta<90`

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

`\sin \theta=(2)/(5)`

Squaring both sides,

`(\sin \theta)^2=((2)/(5))^2`

`\sin^2 \theta=(4)/(25)`

Therefore, The value of
`\sin^2 \theta=(4)/(25)`