Where do the basic trigonometric identities come from

The video tutorial covers the basics of right triangles, the introduction of the XY coordinate system, and the concept of a unit circle. It explains various trigonometric identities, including quotient, reciprocal, and Pythagorean identities. The tutorial also discusses even and odd functions, highlighting the properties of cosine and sine. Finally, it introduces cofunction identities, explaining their relationships and applications in trigonometry.

What is the sine of an angle in a unit circle?

• The angle itself

• The y-coordinate of the point

• The hypotenuse of the triangle

• The x-coordinate of the point

Which of the following is a correct expression for tangent in terms of sine and cosine?

• Tangent = sine / cosine

• Tangent = sine + cosine

• Tangent = cosine / sine

• Tangent = sine * cosine

What is the reciprocal of sine?

• Tangent

• Cotangent

• Cosecant

• Secant

Which identity is represented by the equation: cosine squared plus sine squared equals one?

• Even-Odd Identity

• Quotient Identity

• Reciprocal Identity

• Pythagorean Identity

What happens to an identity if you perform the same operation on both sides?

• It loses its identity

• It becomes invalid

• It becomes a new identity

• It changes form but remains valid

Which function is considered even?

• Sine

• Cotangent

• Cosine

• Tangent

What is the result of sine of negative x?

• Negative sine of x

• Sine of x

• Negative cosine of x

• Cosine of x

Which identity relates sine and cosine with a π/2 shift?

• All of the above

• Sine of π/2 - x = Cosine of x

• Tangent of π/2 - x = Cotangent of x

• Cosine of π/2 - x = Sine of x

What is the cofunction identity for tangent?

• Tangent of π/2 - x = Sine of x

• Tangent of π/2 - x = Cotangent of x

• Tangent of π/2 - x = Secant of x

• Tangent of π/2 - x = Cosine of x

Which of the following is true for an odd function?

• f(-x) = 2f(x)

• f(-x) = f(x)

• f(-x) = -f(x)

• f(-x) = 0