Math Analysis Problem Set 04-01 1. Getting really good at using the Unit Circle will help you to solve a lot of other types of problems. Somehow these have become personal favorites over the years. a. Find all angles x such that cos ( x ) = sin ( 35° ) . b. Find all angles x such that sin ( 265° ) = cos ( x ) . c. Find all angles x such that sin ( 7181° ) = cos ( x ) . d. Find all angles x such that cos ( 544321° ) = sin ( x + 10° ) e. Check all of your answers using a calculator. 2. This contraption is my idea of something that could take water out of a river and dump it in a storage tank.

The buckets are evenly spaced along the circumference of a circle with diameter 20 feet. The wheel rotates at a rate of 11π 30 radians per minute. Each bucket can hold 5 gallons. At time t = 0 , the wheel dumps a bucket of water into a tank. a. How many gallons are dumped in the tank if the wheel runs continuously for 24 hours. b. Give a generalization of the times at which water will be dumped in the tank. c. Turns out the tank has a hole in it! Water leaks from the tank at a rate of 1 5 gallon/min. At the end of 24 hours, how much water is in the tank? d. Why are the answers to a and c not contradictory?

MA Notes 04 Problem Sets

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Math Analysis Problem Set 04-02 Do these. Quickly…like, really fast! 1. These problems make you think about coterminal angles, reference angles, ASTC, cofunctions…yeah…good problems. Rewrite… in terms of… of an angle in quadrant cos ( 35, 783° ) sine III cos ( 665,234° ) cosine II

sin ( 583,281° ) sin ( 61, 322° )

csc ( 55, 423° )

sec ( 54,882° )

tan ( 8,675, 309° ) tan ( 987, 321° )

sine

I

cosine

IV

secant

III

cosecant

II

tangent

IV

cotangent

III

2. This problem makes you use your calculator and makes you think about the trig ratios. Type this on your calculator: {randInt ( −10,10 ) ,randInt ( −10,10 )} . a. Now find the six trig functions of the angle in standard position passing through the point your calculator gave you. If the point reduces, reduce it first to make things easier. b. Find the exact value of the angle passing through the point. Write this in terms of the inverse tangent of the absolute value of the ratio you find for tangent. You will always be using inverse tangent for this so get used to it. c. Find the approximate degree measure of the angle passing through the point. d. Check your answers by verifying the sine and cosine of the angle you found. You probably can’t get approximate to fraction to work on these so don’t bother. Just compare decimal values. e. Repeat until you are completely awesome at this.

MA Notes 04 Problem Sets

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Math Analysis Problem Set 04-03 1. Find the angle/angles between 0 and 360° in the indicated quadrant satisfying the given information. Ratio Quadrant Reference Angle Angle(s)

sin (θ ) = 0.5388

I

sin (θ ) = 0.5388

II

cos (θ ) = −0.5736

III

tan (θ ) = −1.8041

IV

sec (θ ) = 3.9939

IV

cot (θ ) = −2.3559

II

sin (θ ) = −.4578

???

cos (θ ) = .6582

???

2. Find every possible angle satisfying the given information. Ratio Quadrant Reference Angle

sin (θ ) = 0.4688

???

csc (θ ) = 6.3287

II

cos (θ ) = −0.4523

???

sec (θ ) = 2.8119

IV

Angle(s)

3. Find the point at which the terminal side of an angle passing through the given points intersects the unit circle. Do you get it? Given Point Some Work? Unit Circle Point

( 5, 12 ) ( −7, 24 ) ( −3, − 4 ) 4. Given some stuff find some other stuff. Given Quadrant II csc ( t ) = 7 4

sec ( v ) = 12 11 cot ( w ) = 9 4

MA Notes 04 Problem Sets

IV III

Find tan ( t )

csc ( v )

sec ( w ) www.turksmathstuff.com