Chaper 7.2 Flashcards
Opposite side of a triangle
Hypotenuse
Sin of theta
b/c or opposite/hypotenuse
Cos of theta
a/c or adjacent/hypotenuse
Tan of theta
b/a or opposite/adjacent
Csc of theta
c/b or hypotenuse/opposite
Sec of theta
c/a or hypotenuse/adjacent
Cot of theta
a/b or adjacent/opposite
Reciprocal Identities
csc= 1/sin sec= 1/cos cot= 1/tan
Quotient Identities
tan=sin/cos
cot=cos/sin
1=?
sin^2+cos^2
sin^2=
1-cos^2
cos^2=
1-sin^2
Sec^2=
Tan^2 +1
csc^2=
cot^2+1
tan^2=
Sec^2-1
Cot^2=
csc^2-1
Fundamental Identities
tan= sin/cos cot= cos/sin csc= 1/sin sec= 1/cos cot= 1/tan Sin^2 + cos^2=1 Tan^2 +1= sec^2 Cot^2 +1= csc^2
Complementary Angles
Sin= cos(90 degrees-theta) Cos= sin(90 degrees-theta) Tan= Cot(90 degrees-theta) Csc= sec(90 degrees-theta) Sec= csc(90 degrees-theta) Cot= tan(90 degrees-theta)
Right triangle
Has an angle of 90 degrees.
Find cos and csc
Cos=12/13
Csc=13/5
Cos=(square root of 3)/2 find sin
Sin=1/2
Sin^2(20)+cos^2(20)=1
0.16+0.88=1.04
Tan50-sin50/cos50 solve using identities
Tan50-tan50
=0
1-cos^2(20)-cos^2(70) solve using identities
1-sin^2(70)-cos^2(70)
=0