Law Of Sines Flashcards
Law of sins
Sin (A)/ a
Sin angle/ side
How to find h
H= adj (sin angle)
SSA
obtuse
Opp>other
One triangle
SSA solving for h
H=opp one right triangle
H>opp no triangle
H less then opp and other
Two triangles
Area of triangle
Area= 1/2(sin angle)( other sides)
When to use law of cosines
SSS
SAS
Law of cosines
Law of cosines
a^2= b^2+c^2-2(b)(c)(cos A)
When solving SSS
Find the angle opposite of longest side with law of cos
How to find semiperimeter
s= a+b+c/2
Area of triangle when only have SSS
A=| s(s-a)(s-b)(s-c)
s=a+b+c/2
SSA
Obtuse
Opp less than other
No triangle
SSA
Acute
Opp>other
One triangle
SSA
Acute
Opp less than other
Solve for h
Reciprocal identity
Sin Ø
1/csc Ø
Reciprocal identity
Cos Ø
1/sec Ø
Reciprocal identity
Tan Ø
1/cot Ø
Reciprocal identity
Csc Ø
1/sin Ø
Reciprocal identity
Sec Ø
1/cos Ø
Reciprocal identity
Cot Ø
1/tan Ø
Pythagorean identities
Tan sec
1+ tan^2Ø= sec^2Ø
Pythagorean identity
Cot csc
1+ cot^2Ø= csc^2 Ø
Conjunction identities
Sin
Sin(pie/2-ø)=cos Ø
Conjunction identities
Csc
Csc(pie/2-ø)=sec Ø
Confunction identities
Tan
Tan(pie/2-ø)=cot Ø
Confunction identities
Cos
Cos(pie/2-ø)=sin Ø
Confunction identities
Sec
Sec(pie/2-ø)=csc Ø
Confunction identities
Cot
Cot(pie/2-ø)=tan Ø
Which angles negative
(-Ø)aren’t negative
Cos (-Ø)= cos
Sec (-Ø)= sec
