Evaluate an angle using the double angle of cosine from a triangle

The video tutorial explains how to sketch triangles in specific quadrants, focusing on the third quadrant between π and 3π/2. It discusses the properties of tangent, emphasizing why it is positive in this quadrant. The tutorial then introduces the cosine double angle formula, recommending the use of the first formula for most cases. Finally, it covers calculating the hypotenuse using the Pythagorean theorem and evaluates trigonometric functions using this information.

In which quadrant is a triangle located if it is between π and 3π/2?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the orientation of the central angle in a triangle sketch?

• Vertex at the origin, perpendicular to the Y-axis

• Vertex at the origin, perpendicular to the X-axis

• Vertex at the X-axis, perpendicular to the Y-axis

• Vertex at the Y-axis, perpendicular to the X-axis

Why is the tangent positive in the third quadrant?

• Because both opposite and adjacent sides are positive

• Because both opposite and adjacent sides are negative

• Because opposite side is negative and adjacent side is positive

• Because opposite side is positive and adjacent side is negative

Which formula is recommended for the cosine double angle?

• Sine squared of Theta minus cosine squared of Theta

• Sine squared of Theta plus cosine squared of Theta

• Cosine squared of Theta minus sine squared of Theta

• Cosine squared of Theta plus sine squared of Theta

What is the hypotenuse of a triangle with sides 3 and 4?

• 3

• 4

• 5

• 6