Alg II U9.9 Trig DBA
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Nov 24, 2024
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Algebra II Unit 9.9 Trigonometry Discussion-Based Assessment
1.
How do you find the sine, cosine, and tangent values on the unit circle? Provide an
example.
To find the sine value on the unit circle, take the y-coordinate of the point where the terminal
side intersects the unit circle.
Example: For an angle of 30 degrees, the sine value is 0.5.
To find the cosine value on the unit circle, take the x-coordinate of the point where the terminal
side intersects the unit circle.
Example: For an angle of 45 degrees, the cosine value is 0.707.
To find the tangent value on the unit circle, divide the sine value by the cosine value.
Example: For an angle of 60 degrees, the tangent value is approximately 1.732.
2.
Provide an example of a trig function and describe how it is transformed from the
standard trig function f(x) = sin x, f(x) = cos x, or f(x) = tan x using key features.
Example: Let's consider the standard trigonometric function f(x) = sin(x).
Transformation: We can transform this function by applying key features such as amplitude,
period, phase shift, and vertical shift.
Amplitude: Multiply the function by a constant A to change the amplitude. For example, if we
multiply by A = 2, the transformed function becomes g(x) = 2sin(x).
Period: Multiply the argument of the function by a constant B to change the period. For example,
if we multiply by B = 2, the transformed function becomes g(x) = sin(2x).
Phase Shift: Add a constant C to the argument of the function to introduce a horizontal shift. For
example, if we add C = π/4, the transformed function becomes g(x) = sin(x + π/4).
Vertical Shift: Add a constant D to the whole function to introduce a vertical shift. For example, if
we add D = 1, the transformed function becomes g(x) = sin(x) + 1.
By applying these transformations, we can modify the standard trigonometric function to create
various new functions with different properties.
3.
Where does the Pythagorean Identity sin2 Θ + cos2 Θ = 1 come from? How does it
relate to right triangles?
The Pythagorean Identity sin²Θ + cos²Θ = 1 comes from the Pythagorean theorem, which
relates the sides of a right triangle. It shows that the sum of the squares of the sine and cosine
of an angle in a right triangle is always equal to 1.
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