Exploring the Pythagorean Trig Identity

What is the range of angle theta in radians?

• Between 0 and π/2

• Between π and 2π

• Between -π/2 and -π

• Between -3π/2 and -π

What is the value of sine theta given in the problem?

• 2/3

• 1/2

• 3/4

• 1/3

Using the Pythagorean identity, what is cosine squared theta when sine theta is 1/2?

• 1/2

• 1

• 3/4

• 1/4

What are the possible values of cosine theta?

• ±√3/2

• ±1/2

• ±2/3

• ±3/4

In which quadrant is angle theta located based on the given conditions?

• Second

• Fourth

• Third

• First

What is the correct sign of cosine theta in this context?

• Positive

• Negative

• Zero

• Undefined

What is the expression for tangent theta in terms of sine and cosine theta?

• 1 / (sine theta * cosine theta)

• cosine theta / sine theta

• sine theta / cosine theta

• sine theta * cosine theta

What is the simplified form of tangent theta?

• -1/√3

• √3/3

• -√3/3

• 1/√3

Why do we rationalize the denominator in the expression of tangent theta?

• All of the above

• To make it a whole number

• To eliminate the radical from the denominator

• To simplify the expression

What does the tangent of an angle represent in a unit circle?

• Circumference of the circle

• Radius of the circle

• Area of the circle

• Slope of the line intersecting the circle