Trigonometric Functions and Triangle Properties

The video tutorial covers unit circle trigonometry, starting with an introduction to projectile motion and the unit circle. It explains special right triangles, their properties, and how they relate to the unit circle. The tutorial then demonstrates how to use the unit circle to find exact values of trigonometric functions, including sine, cosine, and tangent. It also discusses co-terminal angles and trigonometric identities, providing examples and calculations to illustrate these concepts.

What is the horizontal distance traveled by a golf ball hit at an angle of 50° with an initial speed of 105 ft per second?

• 500 ft

• 250 ft

• 400 ft

• 339 ft

In a 45-45-90 triangle, if the short side is 1, what is the length of the hypotenuse?

• 1

• √2

• 2

• 1/2

In a 30-60-90 triangle, if the short side is 1, what is the length of the side opposite the 60° angle?

• √3

• 1/2

• 2

• 1

What are the coordinates of the point at the top of a 30-60-90 triangle in the unit circle when the 30° angle is at the origin?

• (1/2, √3/2)

• (√3/2, 1/2)

• (0, 1)

• (1, 0)

What is the cosecant of 240°?

• -2√3/3

• 2√3/3

• -√3/2

• √3/2

What is the sine of 315°?

• 1

• -1

• √2/2

• -√2/2

What is the tangent of 930°?

• √3

• -√3

• 1

• -1

What is the secant of 2π/3?

• -1/2

• -2

• 2

• 1/2

What is the cosine of 7π/6?

• 1/2

• √3/2

• -√3/2

• -1/2

What is the cotangent of -7π/6?

• -√3

• √3

• -1

• 1