Trigonometry > Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D
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Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D

Main formulas:

  • The Pythagorean theorem: The side lengths of a right triangle satisfy a2 + b2 = c2.
  • The Pythagorean identity: For any angle x, we have sin2 x + cos2 x = 1.

Example 1:

Use the Pythagorean theorem to prove the Pythagorean identity.

Example 2:

If cosθ = 0.47 and θ is in the fourth quadrant, find sinθ .

Example 3:

Verify the following trigonometric identity :
1+cosθ
sinθ
= sinθ
1 − cosθ

Example 4:

Use the Pythagorean identity to prove the Pythagorean theorem.

Example 5:

If sinθ = − [5/13] and θ is in the third quadrant, find cosθ .
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