October 14, 2015
Trig Chapter 7a Day 4
OBJ: to use the sum and difference Identities to
determine the exact values of trig functions.
But first.....let's write those ID's!
I Reciprocal Identities
1
1 sinθ = csc θ
1
4 csc θ = sin θ
1
2 cos θ = sec
θ
5 secθ = 1
1
3 tan θ = cot
θ
1
6 cot θ =tan
cos θ
θ
II Quotient Identities
1
sin
tan θ = cos θ
θ
2
cos
cot θ = sin θ
θ
III Pythag Identites ( the big 3)
1 sin θ + cos θ=1
2
2
2 1 + tan2 θ =sec2 θ
3 1 + cot θ =csc θ
2
2
IV Sum & Difference Identities NEW--NEW--NEW
1 cos (A + B) = cosA cosB - sinA sinB
cos (A - B) = cosA cosB + sinA sinB
or
2 sin(A + B) = sinA cosB + sinB cosA
sin(A - B) = sinA cosB - sinB cosA
or
3
or
October 14, 2015
Suppose I wanted to find the EXACT value of sin 15
What should I do?
o
Hint: does 15 = the sum or difference of two of our "friendly" angles?
So....
o
o
o
o
o
sin15 = sin(45 - 30 ) or sin (60 - 45 )
Let's look at one of those choices, but first write the
formula:
sin(A - B) = sinA cosB - sinB cosA
sin (45 - 30) = sin45cos30 - sin30cos45
October 14, 2015
Lets look at unit circle values we could use to get:
;
Find the indicated value
ex:
October 14, 2015
o
ex: cos195
o
ex: tan165
October 14, 2015
Verify:
o
verify: sin (x + 90 ) = cos x
Assign Ch7day4 pp 459-460 (2-6; 10-12; 36; 38; 39)p 451 (56)