Trigonometric Functions and Inequalities

This video tutorial covers the process of comparing trigonometric functions by hand. It begins with an introduction to the importance of understanding the signs of trig functions in different quadrants and how to find reference angles. The tutorial then explains cofunction identities and the properties of sine and cosine in the first quadrant. It also discusses the properties of inequalities and reciprocal identities. The video concludes with several example problems, demonstrating how to apply these concepts to compare trig functions effectively.

What is the main focus of this video tutorial?

• Learning calculus

• Comparing trigonometric functions by hand

• Solving algebraic equations

• Understanding geometry

In which quadrant are all trigonometric functions positive?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

How do you calculate the reference angle in the second quadrant?

• Theta minus 90 degrees

• 360 degrees minus theta

• Theta minus 180 degrees

• 180 degrees minus theta

What is the cofunction identity for sine?

• Sine of theta equals secant of 90 minus theta

• Sine of theta equals tangent of 90 minus theta

• Sine of theta equals cosine of 90 minus theta

• Sine of theta equals cotangent of 90 minus theta

What happens to the sine value as the angle increases in the first quadrant?

• It decreases

• It becomes negative

• It remains constant

• It increases

What happens to an inequality when you multiply both sides by a negative number?

• The inequality becomes undefined

• The inequality becomes an equation

• The inequality flips

• The inequality remains the same

What is the reciprocal identity for cosecant?

• 1 over cosine

• 1 over tangent

• 1 over sine

• 1 over cotangent

What is the reference angle for 18 degrees in the first quadrant?

• 72 degrees

• 90 degrees

• 180 degrees

• 18 degrees

In which quadrant is the angle 117 degrees located?

• Third quadrant

• First quadrant

• Fourth quadrant

• Second quadrant

What is the reference angle for 268 degrees in the third quadrant?

• 268 degrees

• 180 degrees

• 92 degrees

• 88 degrees