Exploring Adding and Subtracting Rational Expressions

The video tutorial covers the Pythagorean theorem for finding missing sides of right triangles, properties of special right triangles (45-45-90 and 30-60-90), and the six trigonometric functions (sine, cosine, tangent) along with their reciprocals (cosecant, secant, cotangent). It includes examples and applications of these concepts, emphasizing the importance of special angles in trigonometry.

What is the formula for the Pythagorean theorem?

• a^2 + b^2 = c^2

• a^2 / b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 + c^2

What is the length of the hypotenuse in a 45-45-90 triangle if one leg is 10 units?

• 10√2 units

• 20 units

• 10 units

• 5√2 units

In a 30-60-90 triangle, how is the length of the longer leg related to the shorter leg?

• Longer leg = 2 * Shorter leg

• Longer leg = Shorter leg √2

• Longer leg = Shorter leg / 2

• Longer leg = Shorter leg √3

How is the hypotenuse of a 30-60-90 triangle related to the shorter leg?

• Hypotenuse = 2 * Shorter leg

• Hypotenuse = Shorter leg √3

• Hypotenuse = Shorter leg / 2

• Hypotenuse = Shorter leg √2

What is the sine of an angle in a right triangle?

• Hypotenuse / Opposite side

• Opposite side / Hypotenuse

• Adjacent side / Hypotenuse

• Opposite side / Adjacent side

What is the reciprocal of cosine?

• Sine

• Cotangent

• Cosecant

• Secant

What is the secant of an angle in terms of cosine?

• 1 / Cosine

• Cosine / 1

• 1 / Sine

• Sine / 1

If the cosine of an angle is 2/3, what is the sine of that angle?

• 2 / √5

• 1 / 2

• 3 / 2

• √5 / 3

What is the tangent of 45 degrees?

• 1 / √2

• √2

• 1

• √3 / 2

If the adjacent side of a right triangle is 2 units and the hypotenuse is 3 units, what is the length of the opposite side?

• √5 units

• √3 units

• 5 units

• 1 unit