Given that, tanØ=5/12,
Using trigonometric ratio, please solve ;
(1). SinØ
(2). SinØ + Cos Ø
(3). (Sin^2 Ø / Cos Ø)/(Sin^2 Ø + Cos Ø)
(4). 1 + tan^2 Ø
(5). (1 + tan^2 Ø)/(1 - tan^2 Ø)
Given that tanØ = 5/12, we can use trigonometric identities to find the values of the following expressions:
(1) SinØ:
Since tanØ = SinØ/CosØ, we know that SinØ = tanØ * CosØ.
Using the Pythagorean identity, CosØ = 1/sqrt(1 + tan^2Ø) = 1/sqrt(1 + (5/12)^2) = 12/sqrt(144 + 25) = 12/sqrt(169) = 12/13.
Therefore, SinØ = (5/12) * (12/13) = 5/13.
(2) SinØ + CosØ:
SinØ + CosØ = 5/13 + 12/13 = 17/13.
(3) (Sin^2Ø / CosØ) / (Sin^2Ø + CosØ):
[(SinØ)^2 / CosØ] / [(SinØ)^2 + CosØ] = [(5/13)^2 / (12/13)] / [(5/13)^2 + 12/13] = [(25/169) / (12/13)] / [(25/169) + 12/13] = (25/169) / (12/13) / [(25/169) + 12/13] = (25/169) * (13/12) / (25/169 + 12/13) = 25/156 / (25/169 + 12/13) = 25/156 / (25/169 + 156/169) = 25/156 / 181/169 = (25/156) * (169/181) = 25/181.
(4) 1 + tan^2Ø:
1 + tan^2Ø = 1 + (5/12)^2 = 1 + 25/144 = 169/144 = 1.1806.
(5) (1 + tan^2Ø) / (1 - tan^2Ø):
[(1 + tan^2Ø) / (1 - tan^2Ø)] = [(1 + (5/12)^2) / (1 - (5/12)^2)] = (1 + 25/144) / (1 - 25/144) = (169/144) / (144/144 - 25/144) = 169/144 / 119/144 = 169/119 = 1.4202.