Trigonometric Functions and Identities

The video tutorial explains how to solve trigonometric problems involving right triangles. It begins with calculating sine theta over two using a given right triangle with sides 3, 4, and 5. The tutorial then demonstrates how to find cosine theta over two and tangent theta over two using various formulas. A new problem is introduced where tangent theta is given as 5/12, and the video guides through finding sine, cosine, and tangent for this scenario. The tutorial emphasizes understanding the quadrant in which the angle lies to determine the sign of trigonometric functions.

What is the formula for sine theta over 2?

• Plus or minus the square root of one plus sine theta divided by two

• Plus or minus the square root of one minus sine theta divided by two

• Plus or minus the square root of one plus cosine theta divided by two

• Plus or minus the square root of one minus cosine theta divided by two

In which quadrant is the triangle located if both x and y are positive?

• Quadrant III

• Quadrant II

• Quadrant IV

• Quadrant I

What is the value of cosine theta over 2 for the given triangle?

• Root 5 over 5

• 2 root 5 over 5

• 3 root 5 over 5

• 4 root 5 over 5

How do you find tangent theta over 2 using sine and cosine?

• Sine theta over 2 times cosine theta over 2

• Cosine theta over 2 times sine theta over 2

• Sine theta over 2 divided by cosine theta over 2

• Cosine theta over 2 divided by sine theta over 2

What is the alternative formula for tangent theta over 2?

• Cosine divided by 1 plus sine

• Cosine divided by 1 minus sine

• Sine divided by 1 plus cosine

• Sine divided by 1 minus cosine

What is the value of cosine theta for the new problem with tangent theta as 5/12?

• 5 over 13

• Negative 12 over 13

• Negative 5 over 13

• 12 over 13

What is the value of sine theta over 2 for the new problem?

• 5 root 5 over 26

• 5 root 12 over 26

• 5 root 13 over 26

• 5 root 26 over 26

In which quadrant does theta over 2 lie if theta is between pi/2 and pi?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the value of tangent theta over 2 for the new problem?

• 2

• 1

• 1/2

• 5

How is the positivity of sine, cosine, and tangent determined for theta over 2?

• By analyzing the quadrant in which theta over 2 lies

• By analyzing the quadrant in which theta lies

• By analyzing the signs of x and y

• By analyzing the signs of sine and cosine