Solving Angles in Right Triangles with Inverse Trigonometry

The video tutorial explains how to use trigonometric ratios—sine, cosine, and tangent—to solve for unknown angles in right triangles. It introduces the mnemonic SOHCAHTOA to remember these ratios and explains the concept of inverse trigonometric functions, which allow for finding angles when given a ratio. The tutorial includes a practical example of using the inverse sine function to calculate an angle, demonstrating how to input this into a calculator.

What does the mnemonic SOHCAHTOA help us remember?

• The formulas for calculating angles

• The names of trigonometric functions

• The methods for solving quadratic equations

• The relationships between sides of a right triangle

What does the sine of an angle represent in a right triangle?

• Adjacent over hypotenuse

• Opposite over adjacent

• Opposite over hypotenuse

• Hypotenuse over opposite

What side of the triangle is always opposite the right angle?

• Hypotenuse

• Adjacent leg

• None of the above

• Opposite leg

In the context of trigonometry, what does 'adjacent' refer to?

• The side opposite to the angle in question

• The side opposite to the right angle

• The side next to the angle in question, excluding the hypotenuse

• The longest side of the triangle

What is the inverse cosine function used for?

• To determine the length of the opposite side

• To find an angle from a ratio

• To calculate the area of a triangle

• To find the hypotenuse of a triangle

How is the inverse function notation written for cosine?

• cos^(-1)

• cos^(1)

• sin^(-1)

• tan^(-1)

What does the cosine of an angle in a right triangle represent?

• Hypotenuse over adjacent

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Opposite over adjacent

Which function relates the opposite leg to the hypotenuse?

• Sine

• Cosine

• Cotangent

• Tangent

What is the result of using the inverse sine function on the ratio 5/10?

• 90 degrees

• 60 degrees

• 30 degrees

• 45 degrees

How do you access the inverse sine function on a typical calculator?

• It's typically above the sine button, accessed via a second function key

• Inverse functions are not available on calculators

• Directly pressing the sine button

• Using a special function key