Trigonometric Identities and Formulas

This video tutorial covers essential trigonometric identities and formulas, including basic trigonometric ratios, reciprocal and quotient identities, Pythagorean identities, even and odd functions, cofunction identities, double and half angle identities, sum and difference identities, product to sum and sum to product formulas, and the Law of Sines, Cosines, and Tangents. It also explains how to calculate the area of a triangle using trigonometry.

What is the sine of an angle in a right triangle according to the SOHCAHTOA mnemonic?

• Adjacent over Hypotenuse

• Opposite over Hypotenuse

• Adjacent over Opposite

• Hypotenuse over Opposite

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

• Reciprocal Identity

• Quotient Identity

• Cofunction Identity

• Pythagorean Identity

What happens to the sine function when you replace theta with negative theta?

• It becomes negative cosine theta

• It becomes positive sine theta

• It becomes negative sine theta

• It becomes positive cosine theta

Which of the following is a double angle identity for cosine?

• cosine squared theta minus sine squared theta

• 2 sine theta cosine theta

• 2 tangent theta over 1 minus tangent squared theta

• 1 minus 2 sine squared theta

What is the half angle identity for sine theta over 2?

• Plus or minus the square root of 1 plus sine theta over 2

• Plus or minus the square root of 1 minus sine theta over 2

• Plus or minus the square root of 1 minus cosine theta over 2

• Plus or minus the square root of 1 plus cosine theta over 2

Which formula represents the sum of sine alpha and sine beta?

• 2 sine alpha plus beta over 2 times cosine alpha minus beta over 2

• 2 cosine alpha plus beta over 2 times sine alpha minus beta over 2

• 2 sine alpha minus beta over 2 times cosine alpha plus beta over 2

• 2 cosine alpha minus beta over 2 times sine alpha plus beta over 2

What is the Law of Sines used for in a triangle?

• Finding the length of a side given two angles

• Finding the angles given all three sides

• Finding the area of a triangle

• Finding a missing side or angle in a triangle

Which identity is used to express tangent alpha plus beta?

• Tangent alpha plus tangent beta over 1 plus tangent alpha tangent beta

• Tangent alpha minus tangent beta over 1 minus tangent alpha tangent beta

• Tangent alpha minus tangent beta over 1 plus tangent alpha tangent beta

• Tangent alpha plus tangent beta over 1 minus tangent alpha tangent beta

What is the power reducing formula for sine squared theta?

• 1 plus cosine 2 theta over 2

• 1 minus cosine 2 theta over 2

• 1 minus sine 2 theta over 2

• 1 plus sine 2 theta over 2

Which law is useful for finding an angle when all three sides of a triangle are known?

• Law of Sines

• Law of Cosines

• Law of Tangents

• Law of Secants