Trigonometry and the Unit Circle

The video tutorial covers the basics of trigonometry, including the study of angles and the relationships between angles and sides of triangles. It explains the three basic trigonometric functions: sine, cosine, and tangent, and introduces the mnemonic SOHCAHTOA. The tutorial also discusses reciprocal and quotient identities, the unit circle, and how trigonometric functions can be extended to negative angles and angles larger than 90 degrees. It highlights the importance of understanding the signs of functions in different quadrants using the ASTC mnemonic.

Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse?

• Cosine

• Tangent

• Sine

• Secant

What is the reciprocal of the cosine function?

• Cosecant

• Secant

• Cotangent

• Tangent

According to the Pythagorean identities, what does sine squared plus cosine squared equal?

• 0

• 2

• 1

• Sine

In the unit circle, what is the value of the radius?

• Undefined

• 2

• 1

• 0

How is the sine of an angle represented in the unit circle?

• Hypotenuse

• x-coordinate

• y-coordinate

• Radius

Which quadrant has all trigonometric functions positive?

• Quadrant 4

• Quadrant 3

• Quadrant 2

• Quadrant 1

What mnemonic helps remember the signs of trigonometric functions in each quadrant?

• SOHCAHTOA

• Quotient

• ASTC

• Pythagorean