Right Triangle Trigonometry Trigonometry Basics Right Triangle Trigonometry

Review The sin function: sin A = hypotenuse opposite A

Review Review The cosine function. cos A = hypotenuse A adjacent

Review Review The tangent function. tan A = opposite A adjacent

Sine Function Trig Functions and the Calculator Try each of these on your calculator: sin 55° cos10° tan 87°

Inverse Function Inverse Sine Function Using sin-1 (inverse sin): If 0.7315 = sin θ then sin-1 (0.7315) = θ Solve for θ if sin θ = 0.2419

Inverse Cosine Function Using cos-1 (inverse cosine): If 0.9272 = cos θ then cos-1 (0.9272) = θ Solve for θ if cos θ = 0.5150

Inverse Tangent Function Using tan-1 (inverse tangent): If 0.5543 = tan θ then tan-1 (0.5543) = θ Solve for θ if tan θ = 28.64

Review Review These are the only trig functions you will be using in this course. You need to memorize each one. Use the memory device: SOH CAH TOA

Most Common Application: r y θ x

Review Review Solve for x: x = sin 30° x = cos 45° x = tan 20°

Review Review Solve for θ: 0.7987 = sin θ 0.9272 = cos θ 2.145 = tan θ

What if it’s not a right triangle? Law of Cosines - The square of the magnitude of the resultant vector is equal to the sum of the magnitude of the squares of the two vectors, minus two times the product of the magnitudes of the vectors, multiplied by the cosine of the angle between them. R2 = A2 + B2 – 2AB cosθ θ

What if it’s not a right triangle? - Use the Law of Cosines: In any triangle ABC, with sides a, b, and c,