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