Introduction to Trigonometry and Circles Review

Review of circles and Trig

First we start of with rapid fire review, you only have 10 seconds per question, so be quick.

Multiple Choice

If a radius is 5 cm then what is the length of the diameter?

• 10
• 10 cm
• 2.5

• 2.5cm

Multiple Choice

Which segment is the diameter?

• DE

• BO

• AO

• AB

Multiple Choice

Which segment is a radius?

• RO

• AO

• OB

• all the above

Multiple Choice

Use previous knowledge to figure out how to solve for line segment RP. (use Pythagorean theorem)

• 74.45

• $$\approx\ 8.65$$

• $$\approx5.67$$

Multiple Choice

What is the definition of the center of a circle?

• A segment whose endpoints are on a circle.

• An angle whose vertex is the center of a circle.

• The point from which all points on a circle are equidistant.

• Two endpoints on a circle and all of the points on the circle between those two endpoints.

Multiple Choice

Lets remind ourselves, how many degrees are in a circle?

• 180 $$\degree$$

• $$360\degree$$

• $$90\degree$$

• 270 $$\degree$$

Multiple Choice

Lets remind ourselves, how many degrees are there in a triangle?

• 90

• 180

• 270

• 360

Introduction to Trigonometry

It's Just a Bunch of Fractions!!

The angles sometimes have Greek Names

In a right triangle you must be able to name the sides. The hypotenuse is easy! But the legs are named by how close they are to the angle we are looking at:

• The side opposite the angle (OPP)

• The side adjacent to the angle (ADJ)

• The hypotenuse (HYP)

Video on how to identify Hypotenuse, Adjacent, and Opposite Sides.

https://youtu.be/ia6sZNjKLw0

Multiple Choice

What is the hypotenuse of the triangle shown?

• AB

• BC

• AC

• ∠A

Multiple Choice

Which side is adjacent to ∠B?

• AB

• BC

• AC

• ∠C

Multiple Choice

What is the side adjacent to ∠A?

• AB

• BC

• AC

• ∠C

Multiple Choice

What is the side opposite ∠A?

• AB

• BC

• AC

• ∠B

Multiple Choice

What is the hypotenuse of the triangle shown?

• AB

• BC

• AC

• ∠A

Trigonometry Definitions

Trigonometry is just a bunch of fractions with special names.

The fractions are combinations of the hypotenuse, adjacent, and opposite sides we just defined.

For this class you need to know the names of three special fractions: Sine, Cosine, and Tangent.

Definitions

HOW TO REMEMBER THEM:
SOHCAHTOA

S=O/H C=A/H T=O/A

Multiple Choice

Determine the value of tan(C)

• 7 / 25

• 24 / 25

• 25 / 7

• 24 / 7

Multiple Choice

Determine the value of sin(C)

• 7 / 25

• 24 / 25

• 25 / 7

• 24 / 7

Multiple Choice

Determine the value of cos(C)

• 7 / 25

• 24 / 25

• 25 / 7

• 24 / 7

Multiple Choice

Find the value of cos(C).

• 29/20

• 21/20

• 20/29

• 20/21

Multiple Choice

Find the value of sin(A). Yes you have to reduce all fractions...

• 3/4

• 5/4

• 5/3

• 4/5

Multiple Choice

Find the value of tan(X). Yes you have to reduce the fractions.

• 3/4

• 4/3

• 5/3

• 3/5

Multiple Choice

Determine the tan(25)

• $$\frac{b}{c}$$

• $$\frac{b}{8}$$
  

• $$\frac{8}{b}$$
  

• $$\frac{c}{8}$$
  

Multiple Choice

What is the cos(25)?

• 
  

  $$\frac{b}{c}$$

• $$\frac{b}{8}$$
  

• $$\frac{c}{8}$$
  

• $$\frac{8}{c}$$
  

Multiple Choice

What is the sin(25)?

• $$\frac{b}{c}$$  

• $$\frac{b}{8}$$
  

• $$\frac{c}{8}$$
  

• $$\frac{8}{c}$$
  

Multiple Choice

Which of the following equations is correct?

• $$\tan\left(15.7\right)=\frac{h}{2.5}$$

• $$\cos\left(15.7\right)=\frac{h}{2.5}$$
  

• $$\sin\left(15.7\right)=\frac{h}{2.5}$$

• None of the above

Poll

If I am given a triangle I can identify the hypotenuse, adjacent, and opposite sides.

• Always

• Most of the time

• Sometime

• Rarely

Poll

If I am given a triangle I can find the sine, cosine, and tangent of an angle.

• Always

• Most of the time

• Sometime

• Rarely