Trigonometric Ratios and the Unit Circle

The video tutorial explores trigonometric ratios, focusing on sine, cosine, and tangent. It explains their definitions in right-angled triangles and the limitations for angles beyond 90 degrees. The unit circle is introduced as a tool to extend these definitions. The tutorial covers how trigonometric functions behave in different quadrants and introduces the CAST rule to determine the sign of these functions. Finally, it demonstrates how to apply the CAST rule to solve problems involving angles greater than 90 degrees.

What is the definition of sine in a right-angled triangle?

• Opposite side divided by hypotenuse

• Adjacent side divided by hypotenuse

• Adjacent side divided by opposite side

• Hypotenuse divided by opposite side

Why can't the traditional trigonometric ratios be used for angles greater than 90 degrees?

• Because the triangle would not be right-angled

• Because the hypotenuse would be too long

• Because the angles would sum to more than 180 degrees

• Because the opposite side would be negative

In the unit circle, what is the length of the hypotenuse?

• 0

• 1

• Depends on the angle

• 2

In which quadrant are both sine and cosine positive?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant

What does the 'S' in the CAST rule stand for?

• Sine is negative

• Sine is undefined

• Sine is zero

• Sine is positive

How is tangent determined using the unit circle?

• By setting the base to 1

• By setting the angle to 90 degrees

• By setting the opposite side to 1

• By setting the hypotenuse to 1

In which quadrant is only tangent positive?

• Third quadrant

• Fourth quadrant

• Second quadrant

• First quadrant

What is the equivalent acute angle for sine 160 degrees?

• Sine 20 degrees

• Sine 80 degrees

• Sine 40 degrees

• Sine 60 degrees

What is the equivalent acute angle for cosine 160 degrees?

• Cosine 20 degrees

• Negative cosine 20 degrees

• Cosine 40 degrees

• Negative cosine 40 degrees

What is the equivalent acute angle for tangent 160 degrees?

• Tangent 40 degrees

• Negative tangent 20 degrees

• Negative tangent 40 degrees

• Tangent 20 degrees