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Math Analysis Day III. Right Triangle Trigonometry (4.3) 10/4/11 Two thirds of Americans can't do fractions. The other half, just don't care. Author Unknown sin 30 = sin 60 = Sine and cosine are _________________________________ What is tangent’s cofunction? ____________________________ Cofunctions of complementary angles are equal. (θ = acute ) sin(90 - θ) = cos(90 - θ) = tan(90 - θ) = cot(90 - θ) = sec(90 - θ) = csc(90 - θ) = II. Trigonometric Identities Reciprocal Identities: sin θ = cos θ = tan θ = csc θ = sec θ = cot θ = Quotient Identities: tan θ = cot θ = Pythagorean Identities: sin²θ + cos²θ = tan²θ + 1 = 1 + cot²θ = IV. Applications Involving Right Triangles Standard 12.0 - Students use trigonometry to determine unknown sides or angles in right triangles. _______________________________________ Finding all the unknown angles and sides. Example 3 - Using trigonometry to solve a right triangle Solve the triangle if A = 61° and b = 18. Your Turn Solve the triangle if B = 62°30’ and c = 30. Example 4 - Using trigonometry to solve a right triangle In order to estimate the width of the straight river, a surveyor determined the measurements. Find the width of the river. Your Turn Specifications for a loading dock ramp require a rise of 1 foot for each 3 feet of horizontal length. If the ramp has a rise of 5 ft, solve the triangle.