Trigonometric Functions and Circle Geometry

The lesson explains how to evaluate trigonometric ratios for angles between 0 and 360°. It uses a circle with a radius of 5 to demonstrate calculating sine, cosine, and tangent for a point on the circle. The lesson also covers reflecting points across the y-axis and determining trig ratios in the second quadrant, highlighting the negative cosine and tangent values. Finally, it shows how to determine angles using inverse trig functions, emphasizing the importance of quadrant location in calculations.

What is the range of angles for which trigonometric ratios are evaluated in this lesson?

• 0 to 90 degrees

• 0 to 180 degrees

• 0 to 360 degrees

• 0 to 270 degrees

What is the radius of the circle described by the equation x^2 + y^2 = 25?

• 4

• 6

• 5

• 3

Which point is located on the circle with the equation x^2 + y^2 = 25?

• (4, 3)

• (5, 0)

• (3, 4)

• (0, 5)

How can the radius of the circle be confirmed using Pythagoras' Theorem?

• By calculating 3^2 + 4^2

• By calculating 3^2 + 5^2

• By calculating 5^2 + 3^2

• By calculating 4^2 + 5^2

What is the sine of angle Theta in the first quadrant?

• 3/5

• 4/5

• 5/3

• 5/4

What is the cosine of angle Theta in the first quadrant?

• 5/4

• 5/3

• 4/5

• 3/5

What is the tangent of angle Theta in the first quadrant?

• 3/4

• 4/3

• 5/3

• 5/4

How is the angle Theta determined using the sine function?

• By taking the inverse sine of 0.8

• By taking the inverse tangent of 0.6

• By taking the inverse cosine of 0.6

• By taking the inverse sine of 0.6

What happens to the point (4, 3) when it is reflected across the y-axis?

• It becomes (4, -3)

• It becomes (-4, 3)

• It remains (4, 3)

• It becomes (-4, -3)

What is the cosine of angle Theta in the second quadrant?

• -3/5

• -4/5

• 3/5

• 4/5