Trigonometric Functions and Their Properties

The video tutorial explores the variability of triangles based on given cosine values, emphasizing that different triangles can be drawn with the same cosine information. It introduces constraints with cotangent and explains how to determine the correct quadrant for angles. The tutorial also covers the use of reference angles to create triangles in specific quadrants and analyzes cosine values to determine the positivity of the hypotenuse. The session concludes with final calculations of trigonometric values.

What can be said about the variety of triangles that can be drawn given only the cosine of an angle?

• Triangles can only be drawn in the first quadrant.

• Multiple triangles can be drawn with different orientations.

• Triangles must be isosceles.

• Only one specific triangle can be drawn.

When given a trigonometric equation with a constraint, what must be considered?

• The color of the triangle.

• The quadrant where the angle is located.

• The length of the hypotenuse.

• The type of triangle (e.g., scalene, isosceles).

In which quadrants is cotangent negative?

• First and third quadrants.

• Second and fourth quadrants.

• First and second quadrants.

• Third and fourth quadrants.

What are reference angles used for in trigonometry?

• To simplify the calculation of trigonometric functions.

• To determine the type of triangle.

• To find the length of the hypotenuse.

• To determine the color of a triangle.

Why is the hypotenuse always positive?

• Because it is calculated using squares of other sides.

• Because it is the longest side.

• Because it is always in the first quadrant.

• Because it is always adjacent to the angle.

If cosine is positive, which direction should you move on the x-axis?

• Downwards.

• Upwards.

• To the right.

• To the left.

What is the value of sine if the angle is in the fourth quadrant and the opposite side is negative?

• Negative square root of 3 over 2.

• Positive square root of 3 over 2.

• Zero.

• One.

In which quadrant is tangent negative?

• Second quadrant.

• Third quadrant.

• First quadrant.

• Fourth quadrant.

What is the value of secant if cosine is positive?

• Zero.

• Negative.

• Undefined.

• Positive.

What is the relationship between cotangent and cosine in terms of their signs?

• They are always opposite.

• They are always the same.

• They are independent of each other.

• They are both zero.