Small Angle Approximations in Trigonometry

This video tutorial covers the concept of small angle approximation, focusing on sine, cosine, and tangent functions when angles are close to zero. It includes key facts, variations, and several exam-style questions to demonstrate the application of these approximations. The video also discusses the validity of solutions and provides a step-by-step approach to solving related mathematical problems.

What is the small angle approximation for sin(θ) when θ is close to zero?

• 1 - θ²/2

• θ

• θ²

• 0

Which of the following is the small angle approximation for cos(θ)?

• 1 - θ²/2

• θ²

• θ

• 1

For small angles, tan(θ) is approximately equal to:

• θ

• 1 - θ²/2

• θ²

• 0

What is the small angle approximation for sin(3θ)?

• 3θ

• 1 - 3θ²/2

• 3θ²

• 0

How is cos(3θ) approximated for small angles?

• 3θ²

• 1 - 3θ²/2

• 3θ

• 1

For small angles, tan(3θ) is approximately:

• 3θ

• 0

• 1 - 3θ²/2

• 3θ²

In the expression cos(θ) - 1 over θ multiplied by tan(2θ), what is the approximate value when θ is small?

• 1

• -1/4

• 1/2

• 0

What is the simplified form of the expression 2 - 2cos(θ) over tan(θ) - 1 for small θ?

• 0

• 2θ

• θ - 1

• θ + 1

How can the expression 7 + 2cos(2θ) over tan(2θ) + 3 be approximated when θ is small?

• 3 - 2θ

• 2θ + 3

• 3 + 2θ

• 0

What is the value of 7 + 2cos(2θ) over tan(2θ) + 3 when θ is approximately zero?

• 0

• 2

• 1

• 3