Intro+to+Trig

Unit 4 - Intro to Trigonometry

Summary Notes and Rules (Valerie Mendoza) __ Unit Circle __

The unit circle is the circle whose center is at the origin and whose radius is one. The circumfrence of the unit circle is 2Π. An arc of the unit circle has the same length as the measure of the central angle that intercepts that arc. Also, because the radius of the unit circle is one, the trigonometric functions sine and cosine have special relevance for the unit circle. If a point on the circle is on the terminal side of an angle in standard position, then the sine of such an angle is simply the y-coordinate of the point, and the cosine of the angle is the x-coordinate of the point.



The unit circle is the circle with equation x 2 + y 2 = 1. Let s be the length of the arc with one endpoint at (1, 0) extending around the circle counterclockwise with its other endpoint at (x, y). Note that s is both the length of an arc as well as the measure in radians of the central angle that intercepts that arc.

sine(s) = sin(s) = y. cosine(s) = cos(s) = x.  tangent(s) = tan(s) = cosecant(s) = csc(s) =

secant(s) = sec(s) = cotangent(s) = cot(s) =

The trigonometric functions have different signs according to the quadrant in which the angle's terminal side lies. Here is a chart to show these signs. __ Radians __ One full rotation measures 2π or approximately 6.28 radians. Thus 2π radians = 360°; π radians = 180°;π/2 radians = 90o ;π/3 radians = 60o ;π/4 radians = 45o ;π/6 radians = 30o. . It is absolutely essential that you know the equivalent degree and radian measures for all standard angles. This is not difficult if you think of every standard angle as a multiple of one of our four special angles - 30°, 45°, 60°, and 90°. For example, if 30o = 1π/6, then 60o =2π/6,90o =3π/6,etc. If45o =1π/4,then90o =2π/4; =3π/4;and so on.

Theorems (Valerie Mendoza) __Pythagoras theorems__ says that for a right angled triangle, the square of the long side equals the sum of the squares of the other two sides : x2 + y2 = 12

But 12 is just 1, so: x2 + y2 = 1

//(the **equation of the unit circle)**// Also, since x=cos and y=sin, we get: (cos(θ))2 + (sin(θ))2 = 1 (a useful "identity")

Prerequisite Skills (Hollie Bryan) For trigonometry, pre-requisite skills include dividing fractions, removing square roots from the denominator, and special right triangle concepts, focusing on finding side lengths. __ Dividing Fractions: __

(2/3)/(3/5)In order to divide by a fraction, you must multiply by the reciprocal of the second fraction to make it: (2/3) X (5/3). From there, multiply across. 2X3=6; 3X3=9, so the answer is 6/9 which can reduce to 2/3. __ Removing Square Roots from the Denominator: __ (2/√3) X (4/1) -The first thing to do is to treat it as a normal fraction and multiply it out. 2X4=4; √3X1=√3; the answer to the first part is 4/√3, however, a square root can not be left in the denominator. In order to remove it, multiply the fraction by the square root, which would be √3, or: (4/√3) X (√3/√3) -Next, multiply that out to receive your final answer: (4√3/3), since √3 X √3 is equal to √9, or 3. __ Right Triangle Concepts: __
 * This shows the rules for finding the sides of 45° 90° 45° right triangles one the left while the right one shows those for 30° 60° 90° right triangles.

**Practice Problems** : (Drew Lance, Brenden DeArman)

Beginner
 * 1) Cos90 degress
 * 2) Tan45 degrees

On the way
 * 1) Cos240 degrees
 * 2) Sin135 degrees
 * 3) Cot60 degrees

Got it
 * 1) Csc270 degrees
 * 2) Sec-30 degrees
 * 3) radian of 30 degrees
 * 4) radian of 60 degrees

Rockstar
 * 1) radian of -120 degrees

Annotated Bibliography (Madison Couch) __** Trigonometry for Dummies **__ Annotated Bibliography

Sites ( Jonathan Kierns)

Instructional Videos http://m.youtube.com/watch?v=cIVpemcoAlY [] [] [] []

Helpful SItes [] [] [] [] []

Exam Questions (Madison Couch)


 * 1) tan: -300 degrees
 * 2) cot: 210 degrees
 * 3) sin: -45 degrees
 * 4) csc: 30 degrees
 * 5) cot: 4pi/3

=**Jobs & Occupations that Require the Unit Circle** (Tea' D. and Grant Goforth) =

These people deal with earthquakes and how they effect the structure of buildings. These people are very important when it comes to construction. If these people weren't present in the making of buildings then the making of the building will be irrelevant. If a earthquake happened the building will easily collapse. Above is a link that shows what a earthquake engineer does and some of the things that scientists at Pacific Earthquake Engineering Research Center do to improve the buildings and bridges they build so they can be earthquake ready.
 * 1) **Earthquake Safety Engineer**
 * []**

2. **Astronomist** In astronomoy, to calculate the position of the planets we use trigonometry and spherical trigonometry. The geographical concepts of longitude and lattitude use an application of triginometry.