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:
The value of [tex]\sin^2 \theta=\frac{4}{25}[/tex]
Step-by-step explanation:
Given : [tex]\sin \thet=\frac{2}{5}[/tex] and [tex]0<\theta<90[/tex]
To find : The value of [tex]\sin^2\theta[/tex] ?
Solution :
We have given the value of [tex]\sin \thet=\frac{2}{5}[/tex] and [tex]0<\theta<90[/tex]
To find [tex]\sin^2\theta[/tex] we just have to square [tex]\sin\theta[/tex]
[tex]\sin \theta=\frac{2}{5}[/tex]
Squaring both sides,
[tex](\sin \theta)^2=(\frac{2}{5})^2[/tex]
[tex]\sin^2 \theta=\frac{4}{25}[/tex]
Therefore, The value of [tex]\sin^2 \theta=\frac{4}{25}[/tex]
