warm-up 4/1 fill in chart. 0 1 0 – 1 1 0 0 0 undefined 0 (1, 0) (0, 1) (– 1, 0) (0, – 1)
DESCRIPTION
Rigor: You will learn how to evaluate and determine sign of trig functions using the Unit Circle. Relevance: You will be able to solve real world problems using the Unit Circle.TRANSCRIPT
Warm-Up 4/1Fill in chart.
0 1 0 – 1 1 0 – 1 0
0 undefined 0 undefined
x
y
(1, 0)
(0, 1)
(– 1, 0)
(0, – 1)
Rigor:You will learn how to evaluate and
determine sign of trig functions using the Unit Circle.
Relevance:You will be able to solve real world
problems using the Unit Circle.
Trig 4 The Unit Circle
The Unit Circle.
Unit Circle: a circle of radius 1 centered at the origin in the xy-plane.
2 2 1x y
cos1
sin1
x x
y y
cos ,sin
11
𝑥2+𝑥2=1
x
x
2 𝑥2=1
𝑥2=12
𝑥=√ 12
𝑥= 1√2
=√22
√22
√22
12
x
12
2
+𝑥2=1
𝑥2=1 − 14
𝑥2=34
𝑥=√ 34 =√3
2
√32
0
90
180
270
360
45135
225 315
30
60120
150
210
240 300
330
0𝜋
𝜋2
2𝜋
𝜋4
3𝜋4
5𝜋4
3𝜋2
7𝜋4
𝜋6
𝜋3
2𝜋3
4𝜋3
5𝜋3
5𝜋6
7𝜋6
11𝜋6
1 0
0 1
– 1 0
0 – 1
Unit CircleDraw in triangles to find the coordinates for each point on the unit circle.
30
cos ,sin
1 12
√32
45
1 √22
√22
60
1
12
√32
(x, y)
Numeratoralways 1
Numeratoralways 1 lessthan denominator
Numeratoralways 1 morethan denominator
Numerator alwaystwice denominatorminus one
Example 1: Find the exact value of each expression. If not defined, write undefined.
a.sin
b. cos
c. tan
¿− 12
¿12
¿− √3
2
− 12
∙ 22 ¿ √3
1=√3
Periodic FunctionsA function y = f(t) is periodic if there exist a positive real number c such that f(t + c) = f(t) forall values of t in the domain of t.
The smallest number c for which f is periodic is called the period of t.
Example 2: Find the exact value of each expression.
a.cos
b. sin()
c. tan
¿cos ( 𝜋4 +2𝜋)
¿ sin (60 ° −360 °)
¿cos 𝜋4 ¿ √22
¿ sin 60 °¿√32
¿ tan( 5𝜋6
+4𝜋 )¿ tan 5𝜋6 ¿
12
− √32
¿− 1√3
¿− √33
Assignment:Trig 4 WS 4-3 SGI, 1-8 all
The Spring SAT Crash Course When: April 9-10 and April 16-17 Time: 2:30-5:30Where: Media Center Cost: $10Register: 3-207, by April 8.
I have 11th grade Pert Scores.
7th Warm-Up 4/1Find the exact values for each expression.
1. sin 60°
2. cos
3. tan 30°
¿ √32
¿ √22
¿
12√32
¿1√3
¿ √33
Numeratoralways 1
Numeratoralways 1 lessthan denominator
Numeratoralways 1 morethan denominator
Numerator alwaystwice denominatorminus one
Example 1: Find the exact value of each expression. If not defined, write undefined.
a.sin
b. cos
c. tan
¿− 12
¿12
¿− √3
2
− 12
∙ 22 ¿ √3
1=√3
Periodic FunctionsA function y = f(t) is periodic if there exist a positive real number c such that f(t + c) = f(t) forall values of t in the domain of t.
The smallest number c for which f is periodic is called the period of t.
Example 2: Find the exact value of each expression.
a.cos
b. sin()
c. tan
¿cos ( 𝜋4 +2𝜋)
¿ sin (60 ° −360 °)
¿cos 𝜋4 ¿ √22
¿ sin 60 °¿√32
¿ tan( 5𝜋6
+4𝜋 )¿ tan 5𝜋6 ¿
12
− √32
¿− 1√3
¿− √33
Assignment:Trig 4 WS 4-3 SGI, 1-8 all
The Spring SAT Crash Course When: April 9-10 and April 16-17 Time: 2:30-5:30Where: Media Center Cost: $10Register: 3-207, by April 8.
I have 11th grade Pert Scores.