3.2 Radians. 3.1 Recap Four steps to evaluating trig functions of special angles: 1) Identify the quadrant the angle terminates. 2) Identify the reference.

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Presentation transcript:

3.2 Radians

3.1 Recap Four steps to evaluating trig functions of special angles: 1) Identify the quadrant the angle terminates. 2) Identify the reference angle. 3) Evaluate the trig function of the reference angle (the chart). 4) Determine the sign (ASTC).

The Reference Angle Theorem – A trig function of an angle and its reference angle differ at most in sign.

Pear Deck

Perform the given operations and simplify the following fractions without a calculator, leaving all fractions improper when possible.

Why are there 360 degrees in a circle?

Lets discuss other ways we could measure a circle? What are some things that are geometrically inherent to a circle (like formulas and whatnot)?

What are radians? Figure out the circumference of the circle. Figure out how big the fraction of the circumference we’re dealing with (arc length). Figure out how many times the radius of the circle fits into that arc. That value is the measure of your angle in radians.

Radian Visual Aid

Radian Investigation – do we notice anything about theta vs. r (radius)?

In summary, radians DO NOT depend on the radius at all (why??) and have very little to do with circles.

You are probably asking yourself “Self, why do we need another way to measure angles if we already have degrees?” A: Because the calculus of trig functions does not work out nicely in degrees but works out brilliantly in radians. You are learning how to work with radians now so that you can work at all in the future.

What is bigger 1 degree or 1 radian?

How to convert angles to radians

Whiteboard Practice

Convert from R to D or D to R If the number has a degree symbol ( o ) then it is an angle measure in degrees. If the number does not have the degree symbol, it is an angle measure in radians. That is a rule for ALWAYS, not just these problems.

TIP Here is how I remember to either multiply by π/180 or 180/π: Angle measures in radians (NOT ALWAYS) are in terms of π (ex: Theta = 3π or π/4). So to convert the angle to degrees you would multiply it by 180/π to divide out π. Angle measures in degrees are almost NEVER in terms of π (ex: Theta = 360 o ). To convert to radians, for every 180 you divide out you want to multiply the angle by π, so multiply by π/180.

Pear Deck

Graded Classwork (13 points)

HW: p. 121, 3, 7, 11, 17, 23, 29, 37, 41, 45, 51, 55, 69, 79, 89