Download Objective: Students will discover the six basic trigonometric functions

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Transcript 
Objective: Students will discover the six basic
trigonometric functions.
Ticket in:
Fill in
all of the
RADIANS.
1
Objective: Students will discover the six basic
trigonometric functions.
Hypotenuse
Opposite
SOHCAHTOA
θ
Adjacent
In your notes, write the three trigonometric ratios that are associated with SOHCAHTOA.
sinθ=
cosθ = tanθ = 2
Objective: Students will discover the six basic
trigonometric functions.
Hypotenuse
Opposite
SOHCAHTOA
θ
Adjacent
If there are SIX trigonometric functions, what do you think the other ratios would be?
3
Objective: Students will discover the six basic
trigonometric functions.
These new ratios complete the six
trigonometric functions.
Match the new ratios with their "titles".
Sine = sin θ
O/H
Cosecant = csc θ
H/O
Cosine = cos θ
A/H
Secant = sec θ
H/A
Tangent = tan θ O/A
Cotangent = cot θ A/O
What do you notice?
4
Objective: Students will discover the six basic
trigonometric functions.
6
θ
x
4
Find the missing side. Then, find the value of the six trigonometric functions of the angle θ.
sin θ = csc θ = cos θ = sec θ = tan θ = cot θ = x = 5
Does this relate to the UNIT CIRCLE?
sin θ = y
cos θ = x
tan θ = y/x
(x, y)
csc θ = 1/y
sec θ = 1/x
1
y
cot θ = x/y
x
(1, 0)
6
Look at the relationship between the functions. Which functions are reciprocals of each other?
sin θ = y
cos θ = x
tan θ = y/x
csc θ = 1/y
(x, y)
sec θ = 1/x
1
y
x
cot θ = x/y
(1, 0)
7
H
θ
O
There are three FUNDAMENTAL IDENTITIES
for trig functions. A
• Reciprocal Identities
• Quotient Identities
• Pythagorean Identities
Today we will work with the first set of fundamental identities
RECIPROCAL IDENTITIES
8
H
θ
O
There are three FUNDAMENTAL IDENTITIES
for trig functions. A
• Reciprocal Identities
9
1
Given:
sinθ = 4/5 and cosθ = 3/5
Find: secθ
10
2
Given:
sinθ = 4/5 and cosθ = 3/5
Find: cscθ
11
3
Given:
sinθ = 4/5 and cosθ = 3/5
Find: tanθ
12
4
Given:
sinθ = 4/5 and cosθ = 3/5
Find: cotθ
13
Homework:
• Do page 833 (8 - 19 all). Give exact
answers only (fractions). Do not
worry about decimal answers.
14
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