Trigonometric Functions and Solutions

The video tutorial explains how to solve the trigonometric equation sine squared t equals two cosine t over the interval from zero to two pi. It begins by substituting sine squared t using a trigonometric identity to form a quadratic equation. The quadratic formula is then applied to find the cosine values. The video further explains how to find the corresponding angles in radians using inverse cosine, resulting in two solutions. The process involves sketching angles and using a calculator to ensure accuracy.

What identity is used to rewrite sine squared t in terms of cosine?

• Sine squared theta plus cosine squared theta equals one

• Sine theta equals cosine theta

• Sine squared theta equals cosine squared theta

• Cosine squared theta equals one minus sine squared theta

What form does the equation take after substituting for sine squared t?

• Linear equation

• Exponential equation

• Logarithmic equation

• Quadratic equation

Why is the quadratic formula used in solving the equation?

• The equation is linear

• The equation is exponential

• The equation does not factor

• The equation is already solved

What is the approximate value of cosine t when using the quadratic formula?

• 0.414

• -1.414

• 1.414

• -0.414

Which trigonometric function is used to find the angle t from cosine t?

• Sine

• Tangent

• Inverse sine

• Inverse cosine

What is the first solution for t in radians?

• 1.1437 radians

• 5.1395 radians

• 0.414 radians

• 2.414 radians

In which quadrant is the second solution for t found?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the approximate value of the second solution for t in radians?

• 6.283 radians

• 5.1395 radians

• 3.1415 radians

• 1.1437 radians

What is the reference angle used to find the second solution?

• 3.1415 radians

• 0.414 radians

• 1.1437 radians

• 2.414 radians

What is the interval over which the solutions are found?

• 0 to pi

• 0 to 2pi

• 0 to 3pi

• 0 to 4pi