Master Evaluating the double angle for Sine, Cosine and Tangent from a right triangle

The video tutorial explains how to evaluate trigonometric functions using double angle formulas. It covers the formulas for sine, cosine, and tangent, and demonstrates how to apply them using a right triangle with given side lengths. The instructor emphasizes the importance of memorizing these formulas for tests and homework, and provides step-by-step calculations for each function.

Why is it important to know the double angle formulas when solving problems involving right triangles?

• They help in calculating the area of the triangle.

• They provide a method to find the perimeter of the triangle.

• They are used to determine the type of triangle.

• They are essential for evaluating trigonometric functions at double angles.

What is the double angle formula for sine?

• sin(2θ) = 1 - 2sin²θ

• sin(2θ) = 2cos²θ - 1

• sin(2θ) = 2sinθcosθ

• sin(2θ) = sin²θ - cos²θ

In the context of a right triangle, what does the sine function represent?

• Opposite over adjacent

• Adjacent over hypotenuse

• Adjacent over opposite

• Opposite over hypotenuse

Which of the following is a valid formula for cosine of double angles?

• All of the above

• cos(2θ) = 2cos²θ - 1

• cos(2θ) = 1 - 2sin²θ

• cos(2θ) = cos²θ - sin²θ

What is the result of applying the formula cos(2θ) = cos²θ - sin²θ to a right triangle with sides 3, 4, and 5?

• 25/25

• 16/25

• 9/25

• 7/25

What is the double angle formula for tangent?

• tan(2θ) = 2tanθ + 1

• tan(2θ) = 1 - tan²θ

• tan(2θ) = tan²θ - 1

• tan(2θ) = 2tanθ / (1 - tan²θ)

When simplifying a fraction divided by another fraction, what is the correct method?

• Subtract the fractions

• Divide the numerators and denominators separately

• Add the fractions

• Multiply by the reciprocal of the denominator