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°

•