Evaluate the half angle of tangent using a triangle

The video tutorial covers the concept of secant in trigonometry, focusing on its application in the third quadrant. It explains the relationship between the hypotenuse, adjacent, and opposite sides of a triangle, emphasizing the importance of sign conventions. The tutorial demonstrates how to simplify radicals, specifically sqrt 8, using the Polygon theorem. It also covers the calculation of tangent using cosine and sine values, and provides a detailed explanation of simplifying complex fractions and rationalizing denominators. The tutorial emphasizes arithmetic skills and simplification techniques throughout.

In the context of the third quadrant, what is the relationship between the hypotenuse and the adjacent side for secant?

• Hypotenuse is negative while the adjacent side is positive

• Hypotenuse is greater than the adjacent side

• Hypotenuse is equal to the adjacent side

• Hypotenuse is less than the adjacent side

What is the simplified form of the square root of 8?

• 4

• 2

• 2 sqrt 2

• sqrt 4

How is the tangent of theta divided by 2 expressed in terms of cosine and sine?

• Cosine of theta over sine of theta

• Sine of theta over cosine of theta

• 1 minus cosine of theta over sine of theta

• 1 plus cosine of theta over sine of theta

What is the cosine of theta if the adjacent side is -1 and the hypotenuse is 3?

• -1/3

• 1/3

• -3

• 3

What is the final simplified form of the expression after rationalizing the denominator?

• 2 sqrt 2

• sqrt 2

• -sqrt 2

• -2 sqrt 2