Trigonometric Functions

Open Ended

What does a coordinate system help us to find?

Multiple Choice

Which of the following is a primary use of trigonometric functions in mathematics?

• Solving quadratic equations

• Measuring angles and lengths in triangles

• Finding the mean of a data set

• Calculating the area of rectangles

Open Ended

List three new vocabulary terms introduced in the lesson that are essential for understanding trigonometry.

Multiple Select

Which of the following are trigonometric functions used to find unknown sides or angles in a right-angled triangle?

• Sine

• Cosine

• Tangent

• Secant

Multiple Choice

What is the value of the right angle in degrees in a right-angled triangle?

• 90°

• 45°

• 60°

• 180°

Multiple Choice

Which side of a right-angled triangle is always opposite the right angle?

• Hypotenuse

• Adjacent

• Opposite

• Base

Fill in the Blank

The side adjacent to angle θ in a right-angled triangle is called the ___ side.

Open Ended

Explain the significance of the symbol θ (theta) in trigonometry and how it is used in right-angled triangles.

Multiple Choice

Which side of the triangle is always opposite to the right angle in a right-angled triangle?

• Hypotenuse

• Adjacent

• Opposite

• Base

Open Ended

How does the labeling of 'opposite', 'adjacent', and 'hypotenuse' change with respect to the angle θ in different right triangles?

Multiple Choice

What is the correct formula for sin θ in a right-angled triangle?

• Opposite / Hypotenuse

• Adjacent / Hypotenuse

• Opposite / Adjacent

• Hypotenuse / Opposite

Multiple Choice

Which of the following represents the formula for cos θ?

• Adjacent / Hypotenuse

• Opposite / Hypotenuse

• Opposite / Adjacent

• Hypotenuse / Adjacent

Fill in the Blank

Fill in the blank: In a right-angled triangle, tan θ = ___ / Adjacent.

Multiple Select

Select all correct trigonometric ratios for a right-angled triangle.

• sin θ = Opposite / Hypotenuse

• cos θ = Adjacent / Hypotenuse

• tan θ = Opposite / Adjacent

• cos θ = Opposite / Hypotenuse

Multiple Choice

What is the value of cos C for the triangle with sides 36, 15, and 39?

• 0.923

• 0.385

• 0.577

• 0.333

Multiple Choice

What is the value of tan A for the triangle with sides 35, 12, and 37?

• 0.343

• 2.917

• 0.857

• 1.200

Fill in the Blank

Round 3.248 to 2 decimal places. Write your answer as ___

Multiple Choice

Which of the following statements correctly describes the rules for rounding to decimal places as shown in the images?

• If the digit to be dropped is less than 5, the previous digit is left unchanged. If the digit to be dropped is 5 or more, the previous digit is raised by one.

• If the digit to be dropped is less than 5, the previous digit is raised by one. If the digit to be dropped is 5 or more, the previous digit is left unchanged.

• Always round up regardless of the digit to be dropped.

• Always round down regardless of the digit to be dropped.

Open Ended

Describe how a scientific calculator can be used to find the value of trigonometric functions such as sin, cos, and tan for a given angle.

Multiple Choice

Which of the following are correct values for sin 62°, cos 60°, and tan 25° rounded to 1 decimal place?

• sin 62° = 0.9, cos 60° = 0.5, tan 25° = 0.5

• sin 62° = 0.8, cos 60° = 0.6, tan 25° = 0.4

• sin 62° = 0.7, cos 60° = 0.6, tan 25° = 0.6

• sin 62° = 0.9, cos 60° = 0.6, tan 25° = 0.4

Fill in the Blank

X = _____° (Given sin X = 0.754, write your answer to the nearest degree)

Multiple Choice

Which of the following triangles can the Pythagorean Theorem be applied to?

• A triangle with a 90° angle

• An equilateral triangle

• An isosceles triangle with no right angle

• Any triangle

Multiple Choice

Given a right triangle with legs of length 5 and 12, what is the length of the hypotenuse?

• 13

• 10

• 17

• 7

Multiple Choice

Which of the following is the correct formula for the Pythagorean Theorem?

• a^2 + b^2 = c^2

• a^2 + c^2 = b^2

• b^2 + c^2 = a^2

• a^2 - b^2 = c^2

Open Ended

Explain how the Pythagorean Theorem can be used to find the missing side of a right triangle when two sides are known.

Fill in the Blank

b = _____ (Given a right triangle with sides 6 and 10, and using a^2 + b^2 = c^2, find b)

Open Ended

After learning about coordinate systems and trigonometric functions, what questions do you still have or what topics would you like to explore further?

Open Ended

What is one real-world application of trigonometric functions that you found interesting or would like to learn more about?