Unit 3 Test I

Match the following vocabulary related to the Unit Circle

• arc length

• the length of the curve formed by an arc

• radian

• an angle whose terminal sides lies on an axis

• radian measure

• the ratio of the arc length formed by an angle divided by the r of that circle

• Pythagorean Identity

• states that the square of the cosine of a given angle + the square of the sine of that angle = 1

• quadrantal angle

• measure of a central angle of a circle that intercepts an arc = in length to the r of that circle

The Law of Sines and the Law of Cosines can be used to do which of the following?

• measure the total degrees of a circle

• determine the pole in a polar coordinate system

• in many interesting cases, take limited given information about a triangle and basic understanding of geometry and find all the angles and lengths of those triangles

• herd clowns into a clown car

Match the following basic trigonometry vocabulary with their definitions:

• unit circle

• the position of an angle havin the vertex at the origin& the initial side along the positive x-axis

• terminal side

• the side of a right triangle opposite the right angle

• hypotenuse

• a circle with a center at (0,0)

• coterminal angles

• description of positive and negative angles in standard position sharing the same terminal side

• standard position

• the side of an angle at which rotation ends

In the context of a Unit Circle:

What is the approximate most accurate simplification of 0.866, one-half [either the y or x half; (x, y)] of a coordinate pair in a cartesian Unit Circle representation, which of course does not reach a Unit Square point like, "(1, 1),"

• 
• 
• 
• 

Which is the most true of the following value applied as a position on the X-axis in the context of that number line (0, 0) through (1, 0)?

• It is ~86.6% of the way to a unit of 1.

• It refers to 86 giraffes marching on Istanbul to seize the means of foliage consumption in the strait of Bosphorus.

• It is ~70% of the way to a unit of 1.

• It refers to 70 rhinos marching on the next Geneva Convention.

• It's 100% of the way to a Unit of 1 but only in the context of a Unit Circle, and not a Unit Square.

Answer explanation

We use the square of 1, 2, or 3 each over 2 in the context of the Unit Circle not because we can control which of those numbers correlate to degrees of common angles like 30, 45, and 60 -- but because these are the most accurate representations of numbers which might or actually do repeat as much as the number, "Pi." So, if 30 goes into 180 six times, please remember for an upcoming question soon what that must mean about 30 degrees converted to radians if 180 is equal to, "Pi radians." Pi.. over .. what integer, as a fraction? Remember, that Pi is whether you realize it or not always also, "One Pi," just as 360 degrees itself is, "Two Pi," and therefore in this context each have a coefficient of one, and subsequently, "two." Thank you.

Being careful to not match colors, but radians for letters a (30 degrees), b (45 degrees), and c (60 degrees) - what matching best completes Quadrant I of the Unit Circle with Radian Measures?

• a

• 
• b

• 
• c

• 

Now, for Quadrant I of the Unit Circle, please complete the coordinates before we move onto finish Degrees to Radians. Recall the importance of Desmos.

Recall the importance of thinking in terms of two number lines intersecting at, "(0, 0)."

b

a

c

Being careful to not match colors, but radians for letters a (120 degrees), b (135 degrees), and c (150 degrees) - what matching best completes Quadrant II of the Unit Circle with Radian Measures?

• c

• 
• a

• 
• b

• 

Answer explanation

Thank you.

Please be prepared for additional unit circle questions on the next test and also throughout the rest of maths in your lives, as it is a vital concept.

Being careful to not match colors, but radians for letters a (210 degrees), b (225 degrees), and c (240 degrees) - what matching best completes Quadrant II of the Unit Circle with Radian Measures?

• c

• 
• b

• 
• a

• 

Being careful to not match colors, but radians for letters a (300 degrees), b (315 degrees), and c (330 degrees) - what matching best completes Quadrant VI of the Unit Circle with Radian Measures?

• b

• 
• c

• 
• a

• 

Answer explanation

Thank you.

Please be prepared for additional unit circle questions on the next test and also throughout the rest of maths in your lives, as it is a vital concept.