Answer:
0.998
Step-by-step explanation:
cos θ = 20/29
sin θ = √29² - 20² / 29 = 21 / 29
sin 2θ = 2 sinθ cosθ = 2 x 21/29 x 20/29 = 0.998
Answer:
Sin2θ = [tex]\frac{840}{841}[/tex]
Step-by-step explanation:
Let's take a right angle triangle ABC.
From triangle ABC,
Cosθ = [tex]\frac{AB}{BC} = \frac{20}{29}[/tex] (Given)
By Pythagoras theorem,
[tex](AC)^{2} + (AB)^{2} = (BC)^{2}[/tex]
[tex](AC)^{2} = (BC)^{2} - (AB)^{2}[/tex]
[tex](AC)^{2} = 29^{2} -20^{2}[/tex]
[tex](AC)^{2} = 841 - 400 = 441\\AC = \sqrt{441} = 21[/tex]
So, Sinθ = [tex]\frac{AC}{BC} = \frac{21}{29}[/tex]
Sin2θ = 2 x Sinθ x Cosθ
= [tex]2\times\frac{21}{29} \times\frac{20}{29}[/tex]
= [tex]\frac{840}{841}[/tex]
