ALEKS Trigonometry

initial - Ray that the rotation starts on

terminal - Ray that the rotation ends on


The distance of that rotation about the vertex of the rays

If the rotation moves clockwise, the angle will be negative

Counter clockwise, positive angle

It does,t it can rotate past a full revolution

Angles that share the same terminal side, but no necessarily the same initial side

2π

2π/4 = π/2

2π/3

vertex at origin and initial side long positive X axis

Angles (in std. Position) whose terminal sides coincide with one of the coordinate axes

The degree is an integer multiple of 90°

The radian measure is an integer multiple of π/2

the acute angle formed by the terminal side of an angle in standard position and the x-axis

soh cah toa

(cos,sin)

use soh cah toa


make sure to use the sin⁻¹,cos⁻¹, and tan⁻¹ functions.

ex: sin⁻¹(10/2) for triangle with opposite side of length 10 and hypotenuse of length 2

1. use pethag. theorem to find the third side

2. Use soh cah toa to find the needed basic identites

3. use the magic hexegon to find the rest.

Just leave it as sqrt(x)/y


NOPE

To find unknown angle:
180-given-90 = unknown

To find unknown sides:
assemble trig ratios, solve for each variable

NO, you put it all under 1

sqrt(2), why?

Because this fraction is dividing one whole (2) by some number that multiplied by itself returns 2. The answer to that division is that number, so sqrt(2)

How many halves in one whole?

2

sqrt(3)/3

fraction divided by a fraction is the numerator multiplied by the denominator with the numerator and denominator of the denominator flipped

To get a coterminal angle you add or subtract a multiple of 2π or 360⁰, this places the terminal side back at that location, though the angle size is different.

place the multiple of 2pi/1, then get common denominator, then add or subtract

because 1 pi is divided into 12 pieces, so 24 would be 2pi

4pi/2 is 2pi

The reference angle of a given angle will be that angle minus either pi/2, pi, 3pi/2, or 2pi depending on which quadrant the angle is in.

this works because you are subtracting all the quadrant amounts leaving only the value of angle from the start of the quadrant the terminal side is in to said terminal side, the definition of the reference angle

IT"S ALWAYS FROM THE POSITIVE

TERMINAL ANGLE IS THE ANGLE FORMED BY THE TERMINAL SIDE AND THE X AXIS

s = rθ

1. Convert the given angle to radians if needed

2. do the equation

just apply the known parts and do algebra.

If you get a number that is "1.3 radians" or something like that, no conversion is needed.

When you divide s by r, that gives you the radian fraction


No, for example. 28 = r(.7) -> 28/.7 = 0.68...
This 0.68 number is the radian number. Dont round it and finish the problem

Radian * 180/pi


"180 degrees per radian"

Given that r = sqrt(x^2+y^2), you can calculate the hypotenus (r) with the given point.

the x of the point corresponds to the length of the horizontal side of the triangle, the y corresponds to the vertical

from there the trig ratios are actually normal. soh cah toa