Quiz 2

X

Cosine

Theorem 10.1 the Pythagorean Identity

For any angle fada, cos squares fada + sin squared fada equals 1

Reference angle

For fada usually denoted a swirly thingy is the acute angle between the terminal side of fada as the x-axis

1 revolution

Has a radian measure of two pi in terms of degrees we have 360 degrees equals 2pi radians and 180 degrees equals pi radians

Radian measure

Let fada be the central angle of a circle of radius r that is subtended by arc s then we say that this of angle fada is s/r. The radian measure of an angle tell us how many radius lengths we need to travel along the circle to subtending the angel fada.

To convert radian measure to degree measure

Multiply by 180 degrees/ pi

To convert from degree measure to radian measure

Multiply by pi/180 degrees

Since d=2r

Pi equals C/2r and 2 pi equals c/r or c= 2 pi r

Unit circle

Pi/ 6 (the square root of three/2, 1/2) pi/4 (the square root of two /two, the square root of two over two) pi/3 (1/2, the square root of three/2) pi/2 (0,1) 2 pi/ 3 (-1/2, the square root of three/2) 3pi/4 (-the square root of two/2, the square root of two) 5pi/6 (-the square root of three pi over 2, 1/2) pi (-1,0) 7pi/6 (-the square root of three pi over two, -1/2) 5pi/4 (-the square root of two over two, negative square root of two over two) 4pi/3 (-1/2, -the square root of three over two) 3pi/2 (0,-1)

Y

Sine

Theorem 10.2 Reference Angle Theorem

Supposed fada is the reference angle for fada. Then cosine fada = plus or minus cosine fada and sine fada = plus or minus fada, where the choices of plus or minus depends on the quadrant in which the terminal side of fada lies.

Definition 10.1

The real number pi is defined to be the ratio of a circle's circumference to it's diameter.