Right Triangle Trigonometry

Degree Mode v. Radian Mode

Symbols Theda – Represents the angle measure Hypotenuse Opposite Side Adjacent Side

Six Trigonometric Ratios 3 Basic Ratios + 3 Reciprocal Ratios What is a reciprocal?

Six Trigonometric Ratios, cont. Basic Trig. Ratio Sine Cosine Tangent Reciprocal Trig. Ratio Cosecant Secant Cotangent It’s a sin to have two c’s.

Three Basic Trig. Ratios SOH-CAH-TOA

Sine (SOH)

Cosine (CAH)

Tangent (TOA)

Trigonometric Functions, cont. 3 Reciprocal Functions Cosecant – Reciprocal of Sine Secant – Reciprocal of Cosine Cotangent – Reciprocal of Tangent Remember, “It’s a sin to have two C’s”

Cosecant – Reciprocal of Sine (“It’s a sin to have two C’s.”)

Secant – Reciprocal of Cosine

Cotangent – Reciprocal of Tangent

Solving for Side Lengths If given one side and one angle measure, then we can solve for any other side of the triangle. 8 x

Solving Right Triangles, cont. 1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? 2. Pick the appropriate trig function to solve for x. 3. Solve for x. 8 x

Solving for Side Lengths, cont. 8 x

Solving Side Lengths, cont. 7 x

Inverse Trigonometric Functions We can “undo” trig ratios Gives us the angle measurement (theta) Represented by a small –1 in the upper right hand corner Ex. 2 nd button → trig ratio

Inverse Trigonometric Functions, cont.

Experiment: Take the sin –1 (0.75) and the csc (0.75). What do you get? **** sin –1 ≠ csc Ѳ !!!!! ****

Your Turn: Solve for theta Round to nearest hundredth

Solving For Angle Measures If given two sides of a triangle, then we can solve for any of the angles of the triangle. 54

Solving for Angle Measures, cont. 1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? 2. Pick the appropriate trig function to solve for 3. Solve for using the inverse trigonometric function 54

Solving for Angle Measures, cont. 54

Your Turn: Complete problems 1 – 6 in the Right Triangle Trigonometry Guided Notes – Part II packet.

Answers