Trigonometry Investigation (12/03/26)

when ‘without calculator’ what must we do when getting final answer?

solver simple way then calculator answer

what axis do sine and cosine represent?

cos → x-coordinate

sin → y-coordinate

“why not mathematically correct?”

the trig ratio is distributed into bracket

trig ratios

sin = y/r

cos = x/r

tan = y/r

distance formula

what to always keep an eye out for? (2)

identities and equal radii (triangle)

what does congruence mean?

angles, sides, and shape is same but size or rotation can be different.

four proofs for congruency

SSS

SAS

ASA

RHS

how to ‘compare’

identify corresp angles

identity formula

sin²θ +cos²θ = 1

if AB ≅CD then..

AB² = PQ²

positive compound angle for cos and tips

cos(A+B) = cosAcosB - sinAsinB

sign flip

positive compound angle for sin and tip

sin(A+B) = sinAcosB +cosAsinA

switch trig

what is a good start, end,, and step for calculator?

-180 : 180 : 45

cos(2A) =

1-2sin²A

sin2A =

2sinAcosA

what to do if graphs are the same?

A = B / C / D

A = D '/ F / G

what to say if graphs do if all equal? (2)

they are the same graph and they coincide

how to “apply compound angles without calculator”

Seperate into two special angles separated by a minus or additon then sub into correct compound angle formual

How to “Use cos(α − β ) to derive a formula for sin(α + β )”

1. Use co-function

2. 2. Sub in angles wherebtheta is

3. But beta with 90 like ((90-A)-B)

4. Sub into cosine compound angle formula

5. Use co-fuctions to form sine compound formula

list co-function

sin(90+A)=cosA

sin(90-A)=cosA

cos(90+A)=-sinA

cos(90-A)=sinA

how to “deduce compound formula”

Set two previously worked out equations equal to each other (distance and cosine rule)

what must you always relate?

cosine and compound formula then expand/simplify