Trigonometric Functions and Identities

The video tutorial covers solving trigonometric expressions using double and half angle formulas. It explains how to evaluate sine, cosine, and tangent of double angles using arc functions, and simplifies expressions using right triangles. The tutorial also demonstrates solving cosine squared and sine squared half angle problems, emphasizing the use of trigonometric identities and quadrant analysis.

What is the value of sine theta if theta is arc cosine four over five?

• 4/5

• 3/5

• 5/4

• 5/3

Which quadrant is used to draw the triangle for cosine of two arc tangent negative 12 over five?

• Quadrant 4

• Quadrant 3

• Quadrant 2

• Quadrant 1

What is the value of cosine theta if theta is arc tangent negative 12 over 5?

• 5/13

• 12/13

• -5/13

• -12/13

What is the formula for tangent of two theta?

• 2 tan theta / (1 - tan^2 theta)

• 2 tan theta / (1 + tan^2 theta)

• tan^2 theta / (1 + 2 tan theta)

• tan^2 theta / (1 - 2 tan theta)

In which quadrant is the triangle drawn for arc cosine negative eight over seventeen?

• Quadrant 1

• Quadrant 4

• Quadrant 2

• Quadrant 3

What is the value of cosine theta if theta is arc sine four over five?

• 5/3

• 4/5

• 3/5

• 5/4

Which formula is used to simplify cosine squared of one half arc sine four over five?

• Half angle formula

• Power reducing formula

• Double angle formula

• Sum and difference formula

What is the final simplified value of cosine squared of one half arc sine four over five?

• 5/4

• 3/5

• 5/3

• 4/5

What is the value of cosine theta if theta is arc cosine seven over 25?

• 7/25

• 18/25

• 25/7

• 25/18

What is the final simplified value of sine squared of one half arc cosine seven divided by 25?

• 25/9

• 18/25

• 9/25

• 25/18