Warm-Up Honors Algebra 2 4/18/18 1. Select each statement that is true about the graph of 𝑓 𝑥 = sin 𝑥+3 −2 . A. amp: 1 B. amp: 2 C. midline: y=2 D. y-int: (0,-2) E. x-int: (0,0) 2. What are the solutions to the equation 2 𝑥 2 −𝑥+1=0? a. 1 4 − 5 4 𝑎𝑛𝑑 1 4 + 5 4 b. 1 4 − 7 4 𝑎𝑛𝑑 1 4 + 7 4 c. 1 4 − 7 4 𝑖 𝑎𝑛𝑑 1 4 + 7 4 𝑖 d. 1 4 − 5 4 𝑖 𝑎𝑛𝑑 1 4 + 5 4 𝑖 3. If 3 𝑥+1 5 = 𝑥+1 𝑎 , for x≥1 ,and a is a constant, what is the value of a? a. 3 10 b. 5 6 c. 5 3 d. 10 3

One (1) radian is the measure of the angle that creates an arc the same length as the radius. (It takes some thinking to figure out what that means, so look at the diagram and think about that for a minute.)

Since the circumference of a circle is 2𝜋𝑟 , arc lengths often have 𝜋 in them. So often (but not always), radian measures have 𝜋 in them too. Radian measures of angles come from the unit circle, which is a circle with the radius of 1. Radians essentially refer to the length of the intercepted arc on a unit circle. For that reason, 0° is the same as 0 radians and 360° is the same as 2𝜋 radians (since that’s all the way around a circle because a circle has 360°).

If we know 0° is 0 radians and 360° is 2𝜋 radians, how many degrees would 𝜋 radians be? How many radians would 90° be? 45°? 135°? 225°? 270°? 315°?

Here’s the way to convert back and forth between degrees and radians. If you know the degrees, multiply by a handy form of 1 that will get rid of the degrees and leave you with radians : 𝝅 𝟏𝟖𝟎° If you know the radians, multiply by a handy form of 1 that will get rid of the radians and leave you with degrees : 𝟏𝟖𝟎° 𝝅

Convert 3𝜋 4 radians into degrees Step 1: Multiply 3𝜋 4 ∙ 180° 𝜋 Example 1: Convert 3𝜋 4 radians into degrees Step 1: Multiply 3𝜋 4 ∙ 180° 𝜋 540𝜋° 4𝜋 Step 2: Simplify (cancel out the 𝜋) 135°

Example 2: Convert 150° into radians Step 1: Multiply 150°∙ 𝜋 180° 150𝜋 180 Step 2: Simplify 5𝜋 6