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Transcript 
13.1 part 1 - Six Trig Functions
Objective: TSW calculate the six
trigonometric ratios.
A few things we will be using…
Pythagorean Theorem: π‘Ž2 + 𝑏2 = 𝑐 2
***Remember that β€œc” is the hypotenuse
opposite the 90 degree angle.
πœƒ - β€œtheta”, you will see this to show an angle
measure.
Rationalize a denominator – no radical in the
bottom of a fraction!
Review rationalizing the denominator
Rationalize the denominator:
1
3
a.
b.
5
3
Who remembers….
β€’ SOHCAHTOA?
The Trig Functions we know…
SOH CAH TOA
sin πœƒ =
π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
OR
𝑦
π‘Ÿ
r
cos πœƒ =
π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
tan πœƒ =
π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
OR
OR
𝑦
π‘₯
y
π‘₯
π‘Ÿ
x
We have 6 trig functions…three we know and
three are new, but can be found using the first
three.
Sine
has an inverse
Cosecant
Cosine
has an inverse
Secant
Tangent
has an inverse
Cotangent
The Trig Functions we know…
SOH CAH TOA
csc πœƒ =
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
OR
π‘Ÿ
𝑦
r
sec πœƒ =
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
tan πœƒ =
π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
OR
OR
π‘₯
𝑦
y
π‘Ÿ
π‘₯
x
Examples: Find the six trigonometric functions for each
triangle.
1.
17
15
πœƒ
8
Examples: Find the six trigonometric functions for each
triangle.
2.
πœƒ
10
6
Examples: Find the six trigonometric functions for each
triangle.
3.
πœƒ
7
5
Examples:
4. find cos πœƒ 𝑖𝑓 tan πœƒ =
3
4
Examples:
5. find 𝑠𝑖𝑛 𝐴 𝑖𝑓 cos 𝐴 =
5
11
Homework
13.1 part 1 page 813 #’s 1-4 ALL, 13-20 ALL
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