unit 5 trigonometry vocabulary

What does ratio mean?

To compare two numbers.

What does rounding mean?

Rounding is changing a number to a simpler one that’s close to it. You pick a place value to round to and look at the digit right after it to decide if it goes up or stays the same.

What’s the rule for rounding?

Look at the digit right after the place you’re rounding:

• 0,1,2,3,4 → stay the same

• 5,6,7,8,9 → round up
  Then drop everything after that digit.

How do you round to the nearest whole number?

Look at the first number after the decimal.

• Example: 7.3 → 7 (3 is less than 5)

• Example: 8.6 → 9 (6 is 5 or more)

How do you round to the nearest tenth?

The tenth is the first number after the decimal. Look at the next number.

• Example: 4.27 → 4.3 (7 is 5 or more → round up)

• Example: 5.84 → 5.8 (4 is less than 5 → stay)

How do you round to the nearest hundredth?

: The hundredth is the second number after the decimal. Look at the next number.

• Example: 7.256 → 7.26 (6 is 5 or more → round up)

• Example: 3.891 → 3.89 (1 is less than 5 → stay)

How do you round to the nearest ten?

Look at the ones digit.

• Example: 63 → 60 (3 is less than 5 → down)

• Example: 47 → 50 (7 is 5 or more → up)

How do you round to the nearest hundred?

Look at the tens digit.

• Example: 342 → 300 (4 is less than 5 → down)

• Example: 368 → 400 (6 is 5 or more → up)

How do you round a measurement to the nearest meter?

Same as rounding whole numbers. Look at the first decimal.

• Example: 12.3 m → 12 m (3 < 5 → stay)

• Example: 12.7 m → 13 m (7 ≥ 5 → round up)

How do you round to the nearest degree?

Look at the decimal part. If it’s 0.5 or more → round up. If less → stay.

• Example: 24.4° → 24°

• Example: 24.5° → 25°

How do I always remember rounding?

Circle the place value → check the number to the right → small stay, big go up → drop the rest.

What type of triangle does trigonometry only work in?

Right triangles only.

Where is the hypotenuse located?

Across from the right angle.

It is always the longest side.

When using trig ratios, where do you stand?

At the acute angle.

You never stand at the right angle.

What are the three sides called in trig?

Opposite

Adjacent

Hypotenuse

How do you identify the opposite side?

It is across from the angle you are standing at.

How do you identify the adjacent side?

It is next to the angle you are standing at, but not the hypotenuse.

How many trig ratios are there in this lesson?

Three

Sine

Cosine

Tangent

Sine formula

sin(angle) = opposite over hypotenuse

Cosine formula

cos(angle) = adjacent over hypotenuse

Tangent formula

tan(angle) = opposite over adjacent

What does SOH stand for?

Sine = Opposite over Hypotenuse

What does CAH stand for?

Cosine = Adjacent over Hypotenuse

What does TOA stand for?

Tangent = Opposite over Adjacent

How do you remember the trig ratios?

Say “SOH CAH TOA”

Think: “soaking a toe”

What is Step 1 when solving a trig problem?

Identify the angle you are standing on.

You never stand at the right angle.

Why does where you stand matter?

Because it determines which side is opposite and which side is adjacent.

What is Step 2?

Label the three sides:

Hypotenuse

Opposite

Adjacent

How do you label the hypotenuse?

It is always across from the right angle

How do you label the opposite side?

It is across from the angle you are standing at.

How do you label the adjacent side?

It is next to the angle you are standing at, but not the hypotenuse.

What is Step 3?

Label the given information and label the missing side as x.

What is Step 4?

Choose the correct trig ratio:

Sine

Cosine

Tangent

Depending on what info you have

When do you use sine?

When you are using opposite and hypotenuse.

sin(angle) = opposite over hypotenuse

When do you use cosine?

When you are using adjacent and hypotenuse.

cos(angle) = adjacent over hypotenuse

When do you use tangent?

When you are using opposite and adjacent.

tan(angle) = opposite over adjacent

What is Step 5?

Set up the equation and solve for x

What should you do after solving?

Make sure you answer the question and include correct labeling.

What is the most common mistake in trig problems?

Not labeling hypotenuse, opposite, and adjacent correctly.

What do you do first when solving for a missing angel?

Identify the angle you are solving for and the sides you know.

Step 2 — How do you pick which trig ratio to use?

Choose sine, cosine, or tangent based on the sides you know:

• Opposite & Hypotenuse → sin

• Adjacent & Hypotenuse → cos

• Opposite & Adjacent → tan

Step 3 — How do you set up the equation?

Plug the known side lengths into the trig ratio formula:

Trig(angle) = known/known

Step 4 — How do you solve for the angle?

Use the inverse trig function on your calculator:

• sin⁻¹(opposite/hypotenuse)

• cos⁻¹(adjacent/hypotenuse)

• tan⁻¹(opposite/adjacent)

Step 5 — What do you do after finding the angle?

Write your answer in degrees (or radians if asked) and check if it makes sense with the triangle.

What is an angle of elevation?

The angle measured upward from a horizontal line to an object. It is always inside the triangle, starting from the bottom.

What is an angle of depression?

The angle measured downward from a horizontal line to an object. It is always outside the triangle, starting from the top.

How do you always start solving problems with elevation and depression?

Draw a horizontal line first, then go up or down to form the triangle. This helps you identify which sides are opposite, adjacent, and the hypotenuse.

Where is the horizontal reference line in these problems?

is the line from where you are standing (eye level) for elevation, or from the top for depression. All angles are measured relative to this line.

Quick tip to remember elevation vs depression

Elevate → look up from the bottom

Depress → look down from the top

What is the learning objective for Unit 5 Lesson 5?

Understand the relationship between sine and cosine of complementary angles and apply it to solve examples.

What are complementary angles in a right triangle?

Two acute angles that add up to 90°.

Example: Angle A + Angle B = 90°

What is the relationship between sine and cosine for complementary angles?

sin(A) = cos(B) and sin(B) = cos(A)

Because the two acute angles of a right triangle add up to 90°.

What are sine and cosine called in this relationship?

Co-functions — the sine of one acute angle is the cosine of its complement.

What does θ (theta) represent in trig problems?

A missing angle in a triangle — like a variable.