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

User Greg Ostry
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2 Answers

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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).

User Balint Pato
by
8.7k points
2 votes

Answer:

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)

User Luke Cardeaux
by
7.3k points

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