Trigonometric Identities and Formulas

The video tutorial introduces the calculation of trigonometric values for special angles like 30°, 45°, and 60°, and extends this to angles that can be expressed as sums or differences of these, such as 15° and 75°. It explores the derivation of the cosine difference and sum formulas using the unit circle and angle transformations. The tutorial concludes with a preview of upcoming content on sine sum and difference formulas.

Which of the following angles can be expressed as the difference of 45° and 30°?

• 90°

• 15°

• 60°

• 75°

What is the cosine of 15° if it is expressed as the difference of 45° and 30°?

• sin 45° cos 30° - cos 45° sin 30°

• sin 45° cos 30° + cos 45° sin 30°

• cos 45° cos 30° - sin 45° sin 30°

• cos 45° cos 30° + sin 45° sin 30°

What is the primary focus when expressing trigonometric functions of angle sums and differences?

• Using only sine functions

• Using basic trigonometric functions like sine and cosine

• Using tangent functions exclusively

• Using logarithmic functions

What geometric shape is used in the proof of the cosine difference formula?

• Rectangle

• Triangle

• Circle

• Square

What is the result of cos(α – β) according to the difference formula?

• sin α sin β - cos α cos β

• cos α cos β + sin α sin β

• cos α sin β + sin α cos β

• cos α cos β - sin α sin β

In the context of trigonometric identities, what is the value of cos(–θ)?

• –sin θ

• cos θ

• sin θ

• –cos θ

What is the relationship between sin(–θ) and sin θ?

• sin(–θ) = sin θ

• sin(–θ) = –sin θ

• sin(–θ) = –cos θ

• sin(–θ) = cos θ

How can the angle α + β be expressed to prove the cosine sum formula?

• As α + β = –α + β

• As α + β = α + (–β)

• As α + β = –α – β

• As α + β = α – (–β)

Which formula is derived using the cosine sum formula?

• Sine difference formula

• Tangent sum formula

• Sine sum formula

• Cosine difference formula

Which of the following is a correct expression for the sine sum formula?

• sin(α + β) = cos α sin β - sin α cos β

• sin(α + β) = cos α cos β - sin α sin β

• sin(α + β) = sin α cos β + cos α sin β

• sin(α + β) = sin α sin β + cos α cos β