Trigonometric Identities and Values

The video tutorial demonstrates how to use sum and difference identities to evaluate the sine of 195°. It begins by identifying known angles and their multiples, then finds combinations that sum to 195°. The sum identity for sine is applied, using known values for sine and cosine of 60° and 135°. The expression is simplified to find the final value for s(195°).

What is the main purpose of using sum and difference identities in trigonometry?

• To find the exact value of unknown angles

• To simplify complex trigonometric expressions

• To convert degrees to radians

• To solve linear equations

Which of the following angles is NOT typically used as a known angle in trigonometry?

• 45°

• 90°

• 100°

• 135°

What is the sum of angles used to express 195° in this video?

• 30° and 165°

• 45° and 150°

• 90° and 105°

• 60° and 135°

Which identity is used to find the sine of a sum of two angles?

• Sine difference identity

• Cosine sum identity

• Tangent sum identity

• Sine sum identity

What is the sine of 60°?

• √2/2

• 0

• √3/2

• 1/2

What is the cosine of 135°?

• 1/2

• -1/2

• √2/2

• -√2/2

In which quadrant does the angle 135° lie?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the cosine of 60°?

• 1/2

• √3/2

• 0

• √2/2

What is the sine of 135°?

• 1/2

• -1/2

• √2/2

• -√2/2

What is the result of multiplying the sine of 60° and the cosine of 135°?

• -√3/4

• √3/4

• -1/4

• 1/4