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°