Trigonometric Concepts and Applications

The video tutorial explores algebraic shifts, focusing on tan theta as an identity of sine over cosine. It includes graphing sine and cosine with shifts, evaluating trigonometric expressions in terms of k, and applying Pythagoras to algebraic expressions. The tutorial emphasizes understanding these concepts through visual aids and logical reasoning.

What is the main challenge when dealing with algebraic shifts in non-numeric expressions?

• They involve complex calculations.

• They require memorization of new formulas.

• They are harder to visualize.

• They make our brains react differently compared to numeric expressions.

How is the tangent function expressed in terms of sine and cosine?

• cosine over sine

• sine over cosine

• sine times cosine

• cosine minus sine

What happens to the sine graph when it is shifted by 90 degrees to the left?

• It becomes a tangent graph.

• It becomes a negative sine graph.

• It becomes a cosine graph.

• It remains unchanged.

What is the result of shifting the cosine graph by 90 degrees to the left?

• It becomes a negative cosine graph.

• It becomes a sine graph.

• It remains unchanged.

• It becomes a tangent graph.

In which quadrant is the angle located when sine is positive and cosine is negative?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant

What is the adjacent side in a right triangle if the opposite side is k and the hypotenuse is 1?

• 1 - k

• k

• Square root of (1 - k^2)

• k^2

How do you determine the cosine of an obtuse angle using a triangle on the Cartesian plane?

• By using the Pythagorean theorem.

• By measuring the angle directly.

• By using the tangent function.

• By using the sine function.

What is the significance of the negative sign in the square root of (1 - k^2) when determining cosine?

• It indicates the angle is in the fourth quadrant.

• It indicates the angle is in the third quadrant.

• It indicates the angle is in the second quadrant.

• It indicates the angle is in the first quadrant.

Why is it important to change variables in trigonometry?

• To translate between different functions.

• To simplify calculations.

• To avoid using the Cartesian plane.

• To memorize fewer formulas.

What is the benefit of translating from cosine to sine or vice versa?

• It simplifies the graphing process.

• It helps in understanding vertical and horizontal movements.

• It reduces the number of calculations.

• It eliminates the need for a calculator.