Warm up #2 02/03/16 Wednesday
• If csc θ = 8/15, find sin θ
• If cot θ = 12/5, find sin θ
• Simplify cos2 x tan2 x + cos2 x
7.2 Verifying Trigonometric Identities
EQ: How do you use the basic trigonometric
identities to verify other identities?
Ex1: Verify that sec2 x – tan x cot x = tan2 x is an
identity.
Tip1: You are only able to work on one side
independently, so choose the complicated side.
Tip2: Take care of the reciprocals first to the same
trig function
You Try:
2
2
1+ tan x
= tan x
csc x sec x
csc x
= csc x sec x
cot x
What’s due?
Page 434: #13, 15, 16, 20, 22, 25
Warm up #3 02/05/16 Friday
• Simplify the expression.
sin(q + p )
cos(q - p )
7.3 Sum and Difference Identities
EQ: How do you use the sum and difference of
the identities for the sine, cosine, and tangent
functions?
Key Formulas (in your formula sheet)
Sum and Difference Identities for the Sine Function
α and β represent the measures of two angles
Ex1: cos 75o
75o = 120o – 45o
cos 75o = cos (120o – 45o)
cos 75o = cos 120o cos 45o – sin 120o sin 45o
æ -1 öæ 2 ö æ 3 öæ 2 ö
cos 75° = ç ÷ç ÷ + ç ÷ç
÷
è 2 ø è 2 ø è 2 øè 2 ø
æ 2ö æ 6ö
cos 75° = ç ÷+ç
÷
è 4 ø è 4 ø
æ- 2 + 6 ö
cos 75° = ç
÷
4
è
ø
You Try!
o
cos 735
Ex2:
23p
tan
tan345°
12
æ 5p p ö
tan ç + ÷
è 3 4ø
5p
p
tan
+ tan
3
4
5p
p
1- tan
tan
3
4
-2 + 3
What’s due?
Page 442: #16, 20, 23, 25,
Warm up #4 02/08/15 Monday
• Use sum or difference identities to find the
exact value of each trigonometric function.
• cos 105o
7.3 Continued…
Sub EQ2: How do you find the exact value using
the sum and difference of the identities?
Ex1: sin (x – y) if sin x = 4/9 and sin y = ¼
• Draw the right triangles and label given 0 < x,y < π/2
• sin (x – y) = sin x cos y – cos x sin y
Ex2: tan (x + y) if csc x = 5/3 and cos y = 5/13 given
the interval 0 < x < π/2 and 0 < y < π/2
tan (x + y) = tan x + tan y
1 – tan x tan y
Sub EQ3: How do you verify that each equation is an
identity.
æp
ö
cos ç + x ÷ = -sin x
è2
ø
æp ö
æp ö
cos ç ÷ cos x - sin ç ÷ sin x
è2ø
è2ø
0 - sin x
What’d due?
• Pg. 443 #26, 28, 31, 34, 35, 37
What’s due?
7-4
Page 454: #15 – 19 odd, 22 – 26 even
7-6
Page 459: #23 – 27 odd, 30, 33, 34, 38 – 40 all,
46