Trigonometry - Finding exact trig ratios using addition formula : ExamSolutions

[@EdNYT]

Using double angle formulaes can be an alternative albeit slightly longer method if you don't like using quadrant diagrams, e.g. making sin(120) equivalent to sin(2x60). Where A = 60, sin(2A), 2sin(A)cos(A), can use the exact triangle values to solve the equation. For cos(120) the same principle applies.

[@Minasiu]

Would this come up as a question, asking us to show without a calculator ?

[@ExamSolutions_Maths]

You could but you should learn this method as suppose you had sinA = 2/3 then cos and tan will not give you exact values on your calculator. Using Pythag. etc and following this method works.

[@stickmanz204]

a good way to remember what sin cos and tan are (opposite over hypotenuse ect.) is SOHCAHTOA= sine-opposite over hypotenuse, cos-adjacent over hypotenuse, tan-opposite over adjacent.

[@chiefs529]

one way i learned for the triangles is making the hypotenuse equal to 1. i find it to be a lot easier. so for the 30-60-90, instead of the hypotenuse being 2, the long leg root 3, and short leg 1, you can simplify it so the hypotenuse is 1, long leg is root 3 divided by 2, and the short leg being 1/2. For the 45-45-90, the short and long leg would be root 2 divided by 2, and the hypotenuse would be 1. i thought this was easier for me, it's what they teach me at my school.

[@ExamSolutions_Maths]

You can. root2/2 is the same as 1/(root2) The calculator rationalises the answers that is why it looks different.

[@ExamSolutions_Maths]

The point about these questions is not to use the calculator but to use values that we should know.

[@ExamSolutions_Maths]

Yes, just do 1/tan (75). tan 75 = tan(30+45) = (tan 30 + tan 45)/(1-tan 30tan45) etc

[@joehillion]

do you know if we have to use those triangles and quadrents/sin graphs to workout values or can we simply use our calculators. because for Q2 on the calculator it shows cos45 as (root2)/2 which makes the answer look different to the one you got.

[@ExamSolutions_Maths]

@naniyoussef yes

[@suyoof1239]

Hello, At 7:30ish when you are finding sin120 using the quarant rule, why can you just find sin 60 using the triangle and its the same as 120. Does that mean if it were since 130, you could find the sine of 50 and it would be the same?

[@lak5499]

hi great video as usual...just a quick question: i used the quadrant rule at the beginning of question 2 so i made sin 165= sin 15 and then just changed that to sin (45-30). i got the same answer as you but just wondering how come u didn't do this way? is my method wrong

[@tgc9642]

I was looking for this comment, I did the same as you. Just seemed more logical!

[@izzah310]

if u guys ever find out lmk

[@treepiii318]

For sin 165 you could simply put that into the calculator and get the answer. Then you inverse the answer to get 15 and then work out that sin 15 = sin (45-30), apply the addition formula to get the same final answer

[@sadmanzaid420]

Hahahahaha

[@584emad]

sir what if we had another value of angle say for example cos 246 or 113.5 or 78.4 ?

[@ExamSolutions_Maths]

These are not multiples or easy combinations of 30, or 45 degrees so you wouldn't be expected to get these.

[@nadia1947]

how can i work out value of x between 0and 360 for 3sin(x+10)=4cos(x-10) by addition foprmulas . i have no idea how to find exact value of sin or cos10?thanks for ur help

[@ayesha7786]

is it a must to know those triangles? :/ if we can just use the calculator instead?

[@ExamSolutions_Maths]

You can use a calculator for doing many calculations, even your tables but it helps if you can learn them as you will find you will work quicker in the long term IMO.

[@nadia1947]

how can i work out cot 75? can i just do tan 75 and then finally incverse the final answer but i m keep getting stuck?

[@omaribrahim3481]

For the sin 165 question, I found sin(30+45) and then added that to sin 90 but it gave me a different answer. Shouldn't it be the same?

[@YoussefMedhatAboutaleb]

for sin (165) i used sin (75 + 90) and it turned out to equal to cos 75 is that okay ?

[@dineshn]

I kno sin60 is sin120 by lookong at the gra0h but am I expected to kno it?

[@dineshn]

Why is sin60=sin120