Trigonometric Concepts in Semicircles

The video tutorial explains the geometric properties of a semi-circle with a radius of one. It covers the formation of triangles within the semi-circle, including isosceles and right triangles, and derives formulas for the sine, cosine, and tangent of angles. The tutorial also applies Thales' theorem to demonstrate the similarity of triangles and provides two formulas for the tangent of half an angle.

What is the initial shape used in the video to explain the trigonometric concepts?

• Square

• Semicircle

• Circle

• Triangle

What is the length of the radius in the semicircle?

• 3

• 1

• 0.5

• 2

What is the length of the chord dropped from the endpoint of the radius?

• Secant of t

• Tangent of t

• Sine of t

• Cosine of t

What is the length of the third leg of the triangle formed by the radius and the chord?

• Sine of t

• Cosine of t

• Cotangent of t

• Tangent of t

What is the length of the remainder of the horizontal radius?

• 1 minus Cosine of t

• 1

• Sine of t

• Cosine of t

What type of triangle is formed by the horizontal diameter and the radius?

• Equilateral

• Scalene

• Isosceles

• Right

What is the supplementary angle to t in the isosceles triangle?

• 180 - t

• t/2

• 2t

• 90 - t

What is the angle of the two equal angles in the isosceles triangle?

• 90

• 180 - t

• t/2

• t

What is the angle inside the highlighted right triangle?

• t

• t/2

• 2t

• 180 - t

What is the formula for the tangent of t/2 derived in the video?

• 1 minus Cosine of t over Sine of t

• Sine of t over 1 plus Cosine of t

• Cosine of t over Sine of t

• Sine of t over Cosine of t