88 Frekari notkun hornafræði

Lykiljöfnur

Sínusreglan	$\frac{s i n ⁡ 𝛼 𝑎 = s i n ⁡ 𝛽 𝑏 = s i n ⁡ 𝛾 𝑐 𝑎 s i n ⁡ 𝛼 = 𝑏 s i n ⁡ 𝛽 = 𝑐 s i n ⁡ 𝛾 sin ⁡ α}{a} = \frac{sin ⁡ β}{b = sin ⁡ γ/c a/sin ⁡ α = b/sin ⁡ β = c/sin ⁡ γ}$
Flatarmál órétthyrndra þríhyrninga	$\frac{A r e a = 1 2 ⁢ 𝑏 ⁢ 𝑐 ⁢ s i n ⁡ 𝛼 = 1 2 ⁢ 𝑎 ⁢ 𝑐 ⁢ s i n ⁡ 𝛽 = 1 2 ⁢ 𝑎 ⁢ 𝑏 ⁢ s i n ⁡ 𝛾 Area = 1}{2 ⁢ b ⁢ c ⁢ sin ⁡ α} = \frac{1}{2 ⁢ a ⁢ c ⁢ sin ⁡ β = 1/2 ⁢ a ⁢ b ⁢ sin ⁡ γ}$

Kósínusreglan	𝑎 2 = 𝑏 2 + 𝑐 2 − 2 ⁢ 𝑏 ⁢ 𝑐 ⁢ c o s ⁡ 𝛼 𝑏 2 = 𝑎 2 + 𝑐 2 − 2 ⁢ 𝑎 ⁢ 𝑐 ⁢ c o s ⁡ 𝛽 𝑐 2 = 𝑎 2 + 𝑏 2 − 2 ⁢ 𝑎 ⁢ 𝑏 ⁢ 𝑐 ⁢ 𝑜 ⁢ 𝑠 𝛾 a 2 = b 2 + c 2 − 2 ⁢ b ⁢ c ⁢ cos ⁡ α b 2 = a 2 + c 2 − 2 ⁢ a ⁢ c ⁢ cos ⁡ β c 2 = a 2 + b 2 − 2 ⁢ a ⁢ b ⁢ c ⁢ o ⁢ s γ
Heronsformúla	A r e a = √ 𝑠 ⁢ ( 𝑠 − 𝑎 ) ⁢ ( 𝑠 − 𝑏 ) ⁢ ( 𝑠 − 𝑐 ) w h e r e 𝑠 = ( 𝑎 + 𝑏 + 𝑐 ) 2 Area = s ⁢ ( s − a ) ⁢ ( s − b ) ⁢ ( s − c ) where s = ( a + b + c )/2

Umreikningsformúlur

c o s ⁡ 𝜃 = 𝑥 𝑟 \to 𝑥 = 𝑟 ⁢ c o s ⁡ 𝜃 s i n ⁡ 𝜃 = 𝑦 𝑟 \to 𝑦 = 𝑟 ⁢ s i n ⁡ 𝜃 𝑟 2 = 𝑥 2 + 𝑦 2 t a n ⁡ 𝜃 = 𝑦 𝑥 cos ⁡ θ = x/r \to x = r ⁢ cos ⁡ θ sin ⁡ θ = y/r \to y = r ⁢ sin ⁡ θ r 2 = x 2 + y 2 tan ⁡ θ = y/x

88 Frekari notkun hornafræði

Sínusreglan	$\frac{s i n ⁡ 𝛼 𝑎 = s i n ⁡ 𝛽 𝑏 = s i n ⁡ 𝛾 𝑐 𝑎 s i n ⁡ 𝛼 = 𝑏 s i n ⁡ 𝛽 = 𝑐 s i n ⁡ 𝛾 sin ⁡ α}{a} = \frac{sin ⁡ β}{b = sin ⁡ γ/c a/sin ⁡ α = b/sin ⁡ β = c/sin ⁡ γ}$
Flatarmál órétthyrndra þríhyrninga	$\frac{A r e a = 1 2 ⁢ 𝑏 ⁢ 𝑐 ⁢ s i n ⁡ 𝛼 = 1 2 ⁢ 𝑎 ⁢ 𝑐 ⁢ s i n ⁡ 𝛽 = 1 2 ⁢ 𝑎 ⁢ 𝑏 ⁢ s i n ⁡ 𝛾 Area = 1}{2 ⁢ b ⁢ c ⁢ sin ⁡ α} = \frac{1}{2 ⁢ a ⁢ c ⁢ sin ⁡ β = 1/2 ⁢ a ⁢ b ⁢ sin ⁡ γ}$

Kósínusreglan	𝑎 2 = 𝑏 2 + 𝑐 2 − 2 ⁢ 𝑏 ⁢ 𝑐 ⁢ c o s ⁡ 𝛼 𝑏 2 = 𝑎 2 + 𝑐 2 − 2 ⁢ 𝑎 ⁢ 𝑐 ⁢ c o s ⁡ 𝛽 𝑐 2 = 𝑎 2 + 𝑏 2 − 2 ⁢ 𝑎 ⁢ 𝑏 ⁢ 𝑐 ⁢ 𝑜 ⁢ 𝑠 𝛾 a 2 = b 2 + c 2 − 2 ⁢ b ⁢ c ⁢ cos ⁡ α b 2 = a 2 + c 2 − 2 ⁢ a ⁢ c ⁢ cos ⁡ β c 2 = a 2 + b 2 − 2 ⁢ a ⁢ b ⁢ c ⁢ o ⁢ s γ
Heronsformúla	A r e a = √ 𝑠 ⁢ ( 𝑠 − 𝑎 ) ⁢ ( 𝑠 − 𝑏 ) ⁢ ( 𝑠 − 𝑐 ) w h e r e 𝑠 = ( 𝑎 + 𝑏 + 𝑐 ) 2 Area = s ⁢ ( s − a ) ⁢ ( s − b ) ⁢ ( s − c ) where s = ( a + b + c )/2

Umreikningsformúlur

c o s ⁡ 𝜃 = 𝑥 𝑟 \to 𝑥 = 𝑟 ⁢ c o s ⁡ 𝜃 s i n ⁡ 𝜃 = 𝑦 𝑟 \to 𝑦 = 𝑟 ⁢ s i n ⁡ 𝜃 𝑟 2 = 𝑥 2 + 𝑦 2 t a n ⁡ 𝜃 = 𝑦 𝑥 cos ⁡ θ = x/r \to x = r ⁢ cos ⁡ θ sin ⁡ θ = y/r \to y = r ⁢ sin ⁡ θ r 2 = x 2 + y 2 tan ⁡ θ = y/x