The Unit Circle Lesson (T.2)

The Unit Circle

SOL T.2

Multiple Choice

Factor x² + 11x + 18

• (x + 11)(x + 7)

• (x + 2)(x + 9)

• (x + 6)(x + 3)

• (x + 10)(x + 8)

Multiple Choice

 $\log\left(\frac{m^3}{n}\right)$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

Multiple Choice

When a right triangle is made within a unit circle, the hypotenuse makes the ______ of the unit circle.

• Radius

• Diameter

• Circumference

• Center

Fill in the Blank

The unit circle is called the unit circle becasue it has a radius of ____ units.

Multiple Choice

True/False: The Unit Circle center is at the origin.

• True

• False

Special Right Triangles

45-45-90 and the 30-60-90

45-45-90

• In a triangle whose angles measure 45deg, 45deg, and 90deg, the hypotenuse has a length equal to the product of  $\sqrt{2}$  and the length of either leg.

• The ratio of the sides are  $a:a:a\sqrt{2}$  

Multiple Choice

What is the length of y in this picture?

• 45

• 5√2

• 90

• 5

Multiple Choice

What is the length of y in this 45-45-90 triangle?

• 8√2

• 4√2

• 4

• 8

Multiple Choice

What is the length of y in this 45-45-90 triangle?

• 8√2

• 4√2

• 4

• 8

30 - 60 - 90

• In a triangle whose angles are 30deg, 60deg, and 90deg, the hypotenuse has a length equal to twice of the shorter leg.

• The longer leg is the product of shorter leg and  $\sqrt{3}$  .

• The ratio of the sides is  $x:x\sqrt{3}:2x$  

Multiple Choice

Find x.

• 22

• $11\sqrt{3}$

• $11\sqrt{2}$

• 11

Multiple Choice

Find x.

• 10

• $10\sqrt{3}$

• $10\sqrt{2}$

• 20

Multiple Choice

• x=10√3 y=30

• x=30√3 y=10

• x=10, y=30√3

• x=30 y=10√3

Why are we looking at special right triangles for the unit circle?

• The special triangles will help you remember the trig functions/ratios of the unit circle.

Multiple Choice

What is the value of sine at 30

• 1/2

• √3 / 2

• 0

• √2 ⁄ 2

Multiple Choice

What is the value of cosine at 330?

• 1/2

• √3 / 2

• 0

• √2 ⁄ 2

Multiple Choice

What is the value of sine at 225?

• 1/2

• √3 / 2

• 0

• -√2 ⁄ 2