Comentarios del Tutor: Elegí esta sesión dado que , a diferencia de la manera en que resolvemos este tipo de problemas en algunas partes de Sudamérica , en EEUU optan por hacerlo utilizando esta «regla» en lugar de emplear la identidad trigonométrica Pitagórica. Además, se utilizan los recursos que se nos sugieren constantemente, chequeo de entendimiento. Un cierre de las sesión adecuado.

Student sec A = -4 , cot B =2/3 with A in QII and B in QIII. Find: Sin 2A cos(A-B) tan B/2 csc A/2

Tutor Welcome! How are you today?

Student im ok. Frustrated

Tutor oh, wellIll help you with this

Student thank you!

Tutor Any ideas about it?

Student I know I will need to use a few different Identities. But im not sure how to find Sin andCos to make them work

Tutor okay , first of all we need to get sin and cos for each angle
let’s think about angle A

Student yes , 1/cos

Tutor right, So how much is cos?

Student -4x?

Tutor we know sec is -4 and you told me sec is 1/cos
so how much is cos?

Student right

Tutor if you have sec you flip it , and you get cos

Student -1/4

Tutor perfect! Now we will use a triangle to get sin

Student i cant believe I didnt get that

Tutor we know cos is adj/hyp right?

Student yes

Tutor so we place the 1 and the 4 , like this…
How can we get the missing side?

Student then solve for b

Tutor yes, how much is it?
great! So how much is sin?
perfect!

Student where did the neg go from cos A

Tutor  now we should work on angle B?
sec was negative and we also know the angle is in quad II is negative there

Student  oh okay, but we dont nee that on the triangle?

Tutor nope its the same

Student oky

Tutor just think about the quadrant

Student ok

Tutor what about B? Ideas?

Student cot = cos/sin

Tutor right

Student so would cos be 2 and sin be 3?

Tutor [09:43] not exactly you should place the values in the triangle

Student [09:54] ok

Tutor and get the hypotenuse
great!
so , how much is sin B? and cos B?
can we leave a root in the denominator?

Student nope

Tutor so?
great!
let me tell you something angle B, Its in quadrant III, what do we know about the sin and cos values in q III?

Student cos is neg  and so is sin

Tutor [15:49] okay, so we place the neg sign for them, now we can get the asked values

Student sin (A+A) is SinAcosA+CosAsinA

Tutor okay , you can plug the values

Student do i include teh negative here?

Tutor yes! How much is that?

Student do they cancel out?

Tutor both are negative
hmmm, you cant do that , you must combine both then you can reduce

Student oh!

Tutor perfect!

Student ok thx

Tutor now let me tell you something we forgot about angle B

Student ok

Tutor its in quadrant III , so what do we know about sin and cos?

Student cos is neg

Tutor and sin?

Student and so is sin

Tutor so we place the neg sign for them

Student i will try the others on my own and log back on if I cannot figure it out

Tutor oh ok  great idea!

Student thank you

Tutor Thank you for using our service
Please, do me the favour of completing the survey and comment before leaving

Student yup

Tutor Have a great day! Bye bye

Student bye

Colaborador: Juan Belluscio, Tutor Argentino de Trigonometría

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Primero utlizaremos la identidad pitagórica.
Luego estableceremos la ecuación =0.

Utilizando el sentido común podremos factorear la ecuación como si fuese una cuadrática. Una vez factoreada resolveremos ambos paréntisesis =0 apra obtener las diferentes soluciones para sinx.

Finalmente chequeando el “Unit Circle” encontraremos todas las soluciones posibles para x entre 0 y 2pi. •Recoredemos que para incluir TODAS las soluciones añadiremos “+2kπ”

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Identidad Pitagórica

Suma y Diferencia

Ángulo doble

Ángulo Medio

Identidades de Composición

Muy pocas veces suelen aparecer, pero en caso de que ocurra estas son las más utilizadas.

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Norte o Sur-ángulo-Este u Oeste
North or South-angle-East or West

Norte o sur indican la dirección principal, luego el ángulo indicará cuantos grados al Este o al Oeste debemos desplazarnos.
Ejemplo: N30ºE , 30º East of North, 30º al este del Norte, lo cual gráficamente sería:

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