Simplifying Trigonometric Expressions

The video tutorial explains how to simplify a given trigonometric expression into a single trigonometric function using two methods. The first method involves converting all trigonometric functions to sine and cosine, simplifying complex fractions by multiplying by the least common denominator. The second method uses common denominators to find differences in the numerator and denominator, then simplifies by multiplying by the reciprocal. Both methods ultimately simplify the expression to secant x.

What is the main goal of the video tutorial?

• To graph trigonometric functions

• To solve trigonometric equations

• To simplify a trigonometric expression to a single function

• To learn about trigonometric identities

Which trigonometric function is secant x converted to?

• 1/sin x

• 1/cos x

• sin x/cos x

• cos x/sin x

What is the least common denominator used to simplify the complex fraction?

• sin x

• 1

• cos x

• cos x * sin x

What is the purpose of multiplying the top and bottom of the complex fraction by the least common denominator?

• To create a new fraction

• To add fractions

• To divide fractions

• To eliminate fractions

What is the result of simplifying the expression after factoring the denominator?

• cos x

• 1/sin x

• 1/cos x

• sin x

What is the final simplified form of the expression?

• tangent x

• sin x

• secant x

• cos x

What is the common factor in the denominator that is factored out?

• cos x

• secant x

• 1

• sin x

In the alternative technique, what is the common denominator used in the numerator?

• sin x

• cos x

• 1

• cos x * sin x

What operation is performed instead of dividing by the second fraction in the alternative technique?

• Addition

• Division by the reciprocal

• Subtraction

• Multiplication by the reciprocal

What does the expression simplify to after using the alternative technique?

• 1/cos x

• 1/sin x

• cos x

• sin x