Trigonometric Formulas and Identities

This video tutorial covers fundamental trigonometry concepts, including basic formulas, the area of a sector, right triangle trigonometry, and various trigonometric identities. It explains the relationships between angles and sides in circles and triangles, introduces reciprocal and quotient identities, and discusses co-function and double angle formulas. Additional trigonometric formulas are briefly mentioned, with a reference to a formula sheet for further study.

What is the formula for arc length in a circle when the angle is in radians?

• S = Theta * R

• S = Theta / R

• S = R / Theta

• S = R * Theta^2

How many radians are there in a full circle?

• pi radians

• 360 radians

• 180 radians

• 2 pi radians

Which formula is used to calculate the area of a sector when the angle is in degrees?

• Area = 1/2 * R * Theta

• Area = Theta / 360 * pi * R^2

• Area = 1/2 * Theta * R^2

• Area = Theta * R^2

In right triangle trigonometry, what does the 'SOH' in SOH-CAH-TOA stand for?

• Sine = Adjacent / Hypotenuse

• Sine = Hypotenuse / Opposite

• Sine = Hypotenuse / Adjacent

• Sine = Opposite / Hypotenuse

What is the reciprocal of the cosine function?

• Cotangent

• Tangent

• Cosecant

• Secant

Which identity represents the Pythagorean theorem in trigonometry?

• All of the above

• 1 + cot^2(Theta) = csc^2(Theta)

• tan^2(Theta) + 1 = sec^2(Theta)

• sin^2(Theta) + cos^2(Theta) = 1

What is the co-function identity for sine?

• sin(90° - Theta) = csc(Theta)

• sin(90° - Theta) = sec(Theta)

• sin(90° - Theta) = tan(Theta)

• sin(90° - Theta) = cos(Theta)

Which of the following is an even trigonometric function?

• cos(Theta)

• sin(Theta)

• tan(Theta)

• csc(Theta)

What is the double angle formula for sine?

• sin(2Theta) = 2tan(Theta)/(1 + tan^2(Theta))

• sin(2Theta) = 1 - 2cos^2(Theta)

• sin(2Theta) = sin^2(Theta) - cos^2(Theta)

• sin(2Theta) = 2sin(Theta)cos(Theta)

Which formula is used for the double angle of tangent?

• tan(2Theta) = 1 - tan^2(Theta)

• tan(2Theta) = tan^2(Theta) - 1

• tan(2Theta) = 2tan(Theta)/(1 + tan^2(Theta))

• tan(2Theta) = 2tan(Theta)/(1 - tan^2(Theta))