trig

tangent (definition)

ratio of the opposite side to the adjacent side (TOA)

SOH CAH TOA are all..

ratios of sides to sides in RIGHT triangles

what value of an angle is tangent 1 and why?

45 because opposite and adjacent sides are equal.

If one angle is 90 the other two are opposite each other and 45 each. Because they are congruent the opposite sides are also congruent. Tangent is opposite to adjacent which would be the two equal sides to each other creating a 1:1 ratio and tangent 1

for what angle values is the tangent less then 1 and why?

Angles less than 45 becuase 45 angles would be 1:1, anything less would ,Ean the opposite side is less than the adjacent side, resulting in a tangent less than 1.

Golden Rectangle

a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle

How can you find the slope of the hypotenuse of a right triangle?

The tangent is the same as the slope because rise over run is the same as opposite over adjacent

NOTE: IT MUST BE NEGATIVE IF DOWN, POSITIVE IF UP

The angle of depression

Angle formed from a horizontal line looking down

The angle of elevation

Angle formed from a horizontal line looking UP

Depression and elevation?

MUST be congruent because horizontal lines are parallel (alternate interior angle theorem)

Tangent word problems

ALWAYS include units

Eyesight/bit on the bottom should be included at the end (added on)

REMEMBER = DEPRESSION down ELEVATION up

DRAW EVERYTHING

Always include UNITS! (Squared if area)

What is tan^-1

"Inverse tangent" (-1 is NOT an exponent but means "inverse")

It is used to find a missing angle. On a calculator you click "2nd" and then "tan" and then enter opposite over (divided by) adjacent, this will give you the angle.

Ex: tan ^-1 (4/7)stands for the angle measure whose tangent is 4/7,

SOH - CAH - TOA

Sine - opposite/hypotenuse

Cosine - Adjacent / hypotenuse

Tangent - opposite/ adjacent

ALL ARE RATIOS OF SIDES OF..

RIGHT

TRIANGLES!

The area of Regular Polygons

When 2 angles are complimentary, the sine of one angle equals

The cosine of its complement

Ex: sin(50) = cos(40), sin (45) = cos(45), sin(60) = cos (30)

Finding the area of a non right triangle

Area formula for triangle using trig

Area = (1/2 ab) sin C

know why

Inverse things

You can type "second" and then any of the SOH, CAH, TOA ratios and then the fraction/ratio between the SOH, CAH, TOA and o two; give you the missing angle one

Theta (zero with stripe in between)

Variable like x used for angles

Fractal

A pattern that is self similar I parts are similar to the whole

Can sine ever be more than 1

NO, NEVER because the opposite can never be longer than the hypotenuse (think Pythagorean theorem)

Law of sines

sinA/a=sinB/b=sinC/c

Basically = opposite leg or part over opposite angle is equal to any other students. It's a mascot thing.

Word problems

Area