Trigonometric Concepts and Simplifications

The video tutorial explains how to find the sine, cosine, secant, cotangent, and tangent of half angles using trigonometric formulas. It covers the use of the unit circle and provides examples for angles like 22.5, 112.5 degrees, and 3π/8. The tutorial emphasizes the importance of understanding when to use positive or negative values in calculations and demonstrates how to simplify trigonometric expressions to obtain exact values.

What is the primary method to find the sine of half an angle if you know the cosine of the full angle?

• Use the secant of the angle

• Use the sine of the full angle

• Substitute into the half-angle formula

• Use the tangent of the angle

Which angles are commonly used on the unit circle for half-angle calculations?

• 15, 30, 45, 60

• 30, 45, 60, 90

• 30, 60, 90, 120

• 45, 60, 75, 90

What is the relationship between cosine and secant?

• They are identical

• They are reciprocals

• They are equal

• They are inverses

How do you find the secant of half an angle using cosine?

• Take the reciprocal of cosine divided by 2

• Add 1 to cosine

• Divide cosine by 2

• Multiply cosine by 2

What is the first step in simplifying the expression for secant of half an angle?

• Subtract from the hypotenuse

• Multiply by the hypotenuse

• Use the Pythagorean theorem

• Find the sine of the angle

What is the result of simplifying 1 over the square root of 9 divided by the square root of 10?

• Square root of 9 over 10

• Square root of 10 over 9

• Square root of 10 over 3

• Square root of 3 over 10

In which quadrant is the angle if both X and Y are positive?

• Fourth quadrant

• Second quadrant

• Third quadrant

• First quadrant

What is the formula for cotangent of theta divided by two?

• Sine of theta over one minus cosine of theta

• One minus sine of theta over cosine of theta

• Cosine of theta over sine of theta

• Cosine of theta over one plus sine of theta

How do you simplify the expression square root of 1 plus cosine 4x divided by 2?

• Use the tangent half-angle formula

• Use the sine half-angle formula

• Use the secant half-angle formula

• Use the cosine half-angle formula

What is the simplified form of cosine of 4x divided by 2?

• Sine of 2x

• Cosine of 2x

• Secant of 2x

• Tangent of 2x