Trigonometry

Another name for isosceles right triangles

45-45-90 triangles

Side ratio of 45-45-90 triangles

1 : 1 : sqrt(2)

Property of 45-45-90 triangles

Similar by SAS

Property of 30-60-90 triangles

Similar by AA

Side ratio of 30-60-90 triangles

1 : sqrt(3) : 2

trigonometry

the study of triangles

Formula for tan(theta)

sin(theta) / cos(theta)

tan(90) is undefined because…

…cos(90) is equal to 0

sin(0) and cos(90) are…

…both equal to 0

sin(90) and cos(0) are…

…both equal to 1

Excluding 0 and 90 degrees, the sin and cos of any angle in a right triangle…

…is between 0 and 1

Equation for the unit circle

x² + y² = 1

Purpose of the unit circle

Defines sin, cos and tan for all real numbers

Any point (x, y) on the unit circle corresponds to an angle theta, where…

x equals cos(theta) and y equals sin(theta)

Angles on the unit circle are measured…

…starting at the positive x-axis

Move counterclockwise along the unit circle…

…to measure positive angles on the unit circle

Move clockwise along the unit circle…

…to measure negative angles on the unit circle

Quadrant I

(pos, pos)

Quadrant II

(neg, pos)

Quadrant III

(neg, neg)

Quadrant IV

(pos, neg)

Complementary Angle Theorem

the sine of any acute angle is equal to the cosine of its complement, and the cosine of any acute angle is equal to the sine of its complement

Another name for inverse trig ratios

arcsin, arccos, arctan

Use for trig functions

To find unknown side lengths

Use for inverse trig functions

To find unknown angle measures

Angles go into the argument of trig funcs, while…

…side ratios go into the argument of inverse trig funcs

Formula for triangle area using two sides and an included angle

A = 1/2absinC

The sine of supplementary angles…

…will always be equal

Value of sin30 and cos60

1/2

In a triangle, the largest angle is…

…always opposite the longest side

In a triangle, the smallest angle is…

…always opposite the shortest side

Law of Sines

the ration between the sine of an angle and the side opposite that angle is constant for each of the 3 angle/side pairs within a triangle

Law of Sines formula

sinA/a equals sinB/b equals sinC/c

When using the Law of Sines, if the given information fits SSA…

…there could be 2 answers, so find the supplement of an angle if one is incorrect

Law of Cosines

c² = a² + b² - 2abcosC

Form of the Law of Cosines to find a

a² = b²+ c² - 2bccosA

Form of the Law of Cosines to find b

b² = a² + c² - 2accosB

The cosine of supplementary angles…

…will always be opposites

Value of cos30 and sin60

sqrt3/2

Value of cos45 and sin45

sqrt2/2

Value of tan30

1/sqrt3 or sqrt3/3

Value of tan45

1

Value of tan60

sqrt3

Equation form for trig ratios

ratio(theta) = side/side

Equation form for inverse trig ratios

ratio^-1(side/side) = theta