Right Triangle Trigonometry

Key Concepts

SOHCAHTOA

• S: Sine = Opposite / Hypotenuse
• C: Cosine = Adjacent / Hypotenuse
• T: Tangent = Opposite / Adjacent
• Helps remember how to calculate sine, cosine, and tangent.

Pythagorean Theorem

• Equation: A^2 + B^2 = C^2
• Applies to right triangles.

Six Trig Functions

• Sine (Sin θ) = Opposite / Hypotenuse
• Cosine (Cos θ) = Adjacent / Hypotenuse
• Tangent (Tan θ) = Opposite / Adjacent
• Cosecant (Csc θ) = 1 / Sin = Hypotenuse / Opposite
• Secant (Sec θ) = 1 / Cos = Hypotenuse / Adjacent
• Cotangent (Cot θ) = 1 / Tan = Adjacent / Opposite

Examples

Finding Missing Sides and Trig Function Values

1. Given: Two sides of a right triangle.
2. Method: Use Pythagorean theorem to find the missing side.
3. Once found, calculate all six trigonometric function values based on the given sides.

Special Right Triangles

• 3-4-5, 5-12-13, 8-15-17, and 7-24-25 triangles.
• Multiples of these ratios also form right triangles.

Solving For Missing Sides

1. Use given sides to find the missing side using Pythagorean theorem.
2. Recognize patterns in special right triangles to quickly identify missing sides.

Finding the Value of an Angle

• Use inverse trig functions when given two sides and looking for the angle:
  • If opposite and adjacent are given, use Tan^-1.
  • If adjacent and hypotenuse are given, use Cos^-1.
  • If opposite and hypotenuse are given, use Sin^-1.

Applications

• Solve practical problems involving angles of elevation and depression.
• Trigonometry coursework, including angles, radians, unit circle, and trigonometric functions.
• Advanced topics include solving trig identities and equations, law of sines and cosines, and graphing trig functions.