Trigonometry > Sine and Cosine Functions
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Sine and Cosine Functions

Main definitions and formulas:

  • When you draw an angle θ (measured in radians) in standard position (i.e. starting on the positive x-axis), the coordinates of its terminal side on the unit circle are the cosine and sine of θ .
  • Master formula for right triangles: SOHCAHTOA!
    sinθ = opposite side
    hypotenuse
    		     cosθ = adjacent side
    hypotenuse
    		     tanθ = opposite side
    adjacent side
  • A function f is odd if f(− x) = − f(x), or equivalently, its graph has rotational symmetry around the origin.
  • A function f is odd if f(− x) = f(x), or equivalently, its graph has mirror symmetry across the y-axis.

Example 1:

Find the cosine and sine of 0, (π/2), π , (3π/2), and 2π .

Example 2:

Draw graphs of the cosine and sine functions. Label all zeroes, maxima, and minima.

Example 3:

A right triangle has short sides of lengths 3 and 4. Find the sine, cosine, and tangent of all angles in the triangle.

Example 4:

Graph the functions f(x) = sin(x + (π /2)) and g(x) = cos(x − (π/2)). For each one, determine if the function is odd, even, or neither.

Example 5:

A right triangle has one leg of lengths 5 and hypotenuse of length 13. Find the sine, cosine, and tangent of all angles in the triangle.

Example 6:

Graph the functions f(x) = sin(x −(π /2)) and g(x) = cos(x + (π /2)). For each one, determine if the function is odd, even, or neither.
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