Radian Measure One radian is the measure of a central angle of a circle that intercepts an arc whose length equals a radius of the circle. What does that mean? r = 12 General Formula or Central angleintercepts an arc whose length, s, isinches in a circle that has a radius length of 12 inches. Find That was easy

Comparing Degrees and Radians The radius of a circle is 12 centimeters. What is the number of centimeters in the length of the minor arc intercepted by a central angle that measures 135 o ? r = 12 s Method 1Method 2 How about that. You get the same answer either way.

Arc Length and Radians

Homework Page 405: 28 – 40 Even Numbers

Trigonometric Functions First, let’s review the three basic Trigonometric Functions. Sine (sin) Cosine (cos) Tangent (tan) Now there’s three more trigonometric functions that you need to know. I remember those. They are called the Reciprocal Functions because each one is a reciprocal of one of the basic three functions. Cosecant (csc) Secant (sec) Cotangent (cot) Remember… One Co No Co Co

Trigonometric Functions & Angles Let’s look at the Trigonometric Functions with a triangle. AC B a b c To get the reciprocal functions, just flip over the basic functions.

Reciprocal Function Relationships Remember… One Co No Co Co

The Unit Circle A Unit Circle is a circle with center at the origin and a radius length of 1. r = 1 x y P(x, y) I think this is probably something very important.

Signs of the Trigonometric Functions The signs of the trigonometric functions depend on the signs of x and y in the quadrant in which the terminal side of the angle lies. Quadrant I (+x, +y) All Positive Quadrant II (-x, +y) Sine Positive Quadrant III (-x, -y) Tangent Positive Quadrant IV (+x, -y) Cosine Positive A S TC +x-x +y -y

Finding the Exact Values of the Trigonometric Functions Find the exact values of the six trigonometric functions given each point on the unit circle. That was easy

More Finding the Exact Values of the Trigonometric Functions Find the exact values of the six trigonometric functions given each point on the unit circle. That was easy

Homework Page 366: 3 – 10 Find the exact value of the six trigonometric functions

Coordinate Trigonometric Definitions If P(x, y) is any point on the terminal side of an angle in standard position and r is the distance of P from the origin, then the six trigonometric functions can be defined in terms of x, x, y, y, and r.r. x y I’m not sure I like the sound of that. That doesn’t sound much better. P(x, y) r x y

Coordinate Trigonometric Example If P(4, -3) is a point on the terminal side of an angle, find the values of the sine, cosine, and tangent of the angle. x y I think I can do this. P(4, -3) 4 -3 r Remember the Pythagorean Theorem. That was easy

Quadrantal Angles An angle rotation of 0 o, 90 o, 180 o, 270 o, or 360 o is a Quadrantal Angle 0 o, 360 o 90 o 180 o 270 o r = 1 (1, 0) (0, 1) (-1, 0) (0, -1) (x, y) 90 o 180 o 270 o 360 o Degrees Radians 1 0 undefined undefined 0 1 0

Homework Page 366: 11 – 14 Page 367: 2 – 8 Even Numbers