•Topic: Trig Propertes

Aim: how can we identify the reference angle given an angle terminating in other than quadrant I on the unit circle?

•Do Now: in a 45-45-90 right traingle, if the hypoutenuse is 1, what is the length of the the two legs?

• 

•Do Now Solution

•Using a 45-45-90 right triangle, if the hypotenuse is equal to 1, what is the length of the other two legs?

•Both legs are equal (45-45-90)

•Leg = 1/√2 = √2/2

•

•Example 2

•Find the cos of 300°

•

•Draw a unit circle and label the radius (=1)

•

•Find the reference angle and refer to CHART

•ALL Students take Chemistry!

•Exact value chart – save to notes

•Example 1: Finding the reference angle

•Find the exact value of sin 120°

•Step 1: Which quadrant? (II)

So, only sin is + ; all others are –

•Step 2: Find reference angle: 180 – 120 = 60° - always makes angle with the x-axis!

• Step 3: identify sin 60° = √3/2 (see prev chart)

•Step 4: synthesize steps 1-3.

•

•Therefore, the sin 120° = - √3/2

•Exit slip

Point            is  on  the unit circle

 whose center is the origin.  If Θ is an angle in standard position whose terminal ray passes through point A, what is the value of  sin Θ?

Topic: Trig Properties

Aim: How can we find exact values of cos and sin of 30°, 45°, and 60°angles using the unit circle?

•Do Now:

•What is the exact value of the cos 30°?

the exact value of the sin 30°? Use the chart from yesterday

  

•Exact value chart – save to notes

•Find the exact value of cos 120°

•Step 1: Which quadrant? (II)

So, only sin is + ; all others are –

•Step 2: Find reference angle: 120 – 90 = 30° - always makes angle with the x-axis!

• Step 3: identify cos 30° = √3/2 (see prev chart)

•Step 4: synthesize steps 1-3.

•

•Therefore, the cos 120° = - √3/2

•Example 1: Finding the reference angle

•ALL Students take Chemistry!

•Reference angle continued

•The sin 60° is √3/2, so the sin 240° = -√3/2

•

•The cos 60° is ½, so the cos 240° = - ½

•

•Note: don’t use the ref angle in your final answer, but the original angle instead

•

•Use the unit circle and Right triangles

•30-60-90 Right triangle

•45-45-90 Right triangle

•

•

•Final Assessment

•Using a 45-45-90 right triangle, if one of the legs is equal to 7cm, what is the length of the other leg and the hypotenuse?

•

•Exit slip

•Find the sin and cos of 225°

•

•Draw a unit circle and label the radius (=1)

•

•Inscribe a right triangle using an angle of 45°

•

Finding exact values of cos and sin

Topic: Trig Properties

Aim: How can we find exact values of cos and sin of 30°, 45°, and 60°angles using the unit circle•

•Do Now:

•What is the exact value of the cos 45°?

the exact value of the sin 45°

•Finding exact value of cos 45°

•Use Pythagorean theorem knowing the hypotenuse = 1

•Cos 45° = length of equal leg = √2/2

•Sin 45° = √2/2

•Cos 60° = x = length of shorter leg = ½

•Sin 60° = length of longer leg = √3/2

•Exact value chart – save to notes

•ALL Students take Chemistry!

•Find the exact value of cos 120°

•Step 1: Which quadrant? (II)

So, only sin is + ; all others are –

•Step 2: Find reference angle: 120 – 90 = 30°

• Step 3: identify cos 30° = √3/2 (see prev chart)

•Step 4: synthesize steps 1-3.

•

•Therefore, the cos 120° = - √3/2

•Using the graphing calculator

•Find the MODE button

•Press and make sure “DEGREE” is highlighted (not RADIAN)

•Press cos, then input the angle and press ENTER

•Round your answer to the nearest ten-thousandth (which is 4 decimal places to the right)

•Use the unit circle and Right triangles

•30-60-90 Right triangle

•45-45-90 Right triangle

•Exit slip

•Find the sin and cos of 225°

•Draw a unit circle and label the radius (=1)

•Inscribe a right triangle using an angle of 45°

Angles and the Unit Circle Day 2

Topic: Angles and The Unit Circle Aim: How do we calculate the cosine and sine of an angle?
Do Now: Describe coterminal angles and give an example of two angles that are coterminal. Sketch them.
2 Day Lesson Plan
All worksheets must have your name on it
They must ALL be dropped in the white basket before the end of the period OR you will receive NO CREDIT for your work!!!
Vocabulary
Standard position
Initial side
Terminal side
Coterminal angles
Unit circle
Cosine of θ
Sine of θ
Coterminal angles
Problem 3 Page 830 Handout
Why is 60° not coterminal with the other three angles?

Try the “Got it” #3


Unit Circle
Radius of 1
Center at origin of the coordinate plane
Points on the unit circle are related to periodic functions
Use Greek letter theta θ for angle measure.

Cosine and Sine of an angle
The cosine of θ (cosθ) is the x coordinate of the point at which the terminal side of the angle intersects the unit circle.
The sine of θ (sin θ) is the y-coordinate.
Exit slip
Page 345 Handout

Standardized Test Prep

Questions 1-4
Classwork
Page 347 handout

#1 -11, 12 – 15

Page 348 Handout 43 – 45, 52-54, 55, 61