Much easier to understand than that CAST diagrams books and teachers always bang on about! Also random question but where did the whole concept come from with sin , cos, tan? In the real world would you need ti use the graphs of these functions?
The calculator only gives you the solution between -90 degrees and 90 degrees when you use inverse tan. So you need to add 180 degrees to get the obtuse angle.
The proof of each trigonometric function shows that sin(x) is the value of the height of the triangle, the cosine(x) is the width and the tan(x) is the gradient. So when we are working out in this question the values of tan and cosine we input them into the ratio given by SohCahToa and not just simply out them as either the height, width or gradient? Can someone please expalin my confusion as i feel the two rules are contradictory. I feel it has somthing to do with the radius being the value of one in the proof example?
sin(x) is the height and cos(x) is the base of a right-angled triangle with angle x, IF the hypotenuse is of length 1. Otherwise, sin(x) = opp/hyp, cos(x) = adj/hyp as from SOHCAHTOA.
tan(x-40) = 1.5 x-40 = arctan(1.5) = 56.30993247 x = 96.30993247 Then add/subtract 180 to this value to collect any other solutions. x = 96.3... - 180 = -83.69006753 so x = {-83.7,96.3} to 1dp
![A-Level Maths: E1-07 [Trigonometry: EXTENSION Proof of the Sine Rule]](http://i.ytimg.com/vi/kKiU6NgUQBI/mqdefault.jpg)
![A-Level Maths: E1-07 [Trigonometry: EXTENSION Proof of the Sine Rule]](/img/tr.png)
![A-Level Maths: E3-01 [Trig Graphs: Sketching sin(x), cos(x) & tan(x) from the Unit Circle]](http://i.ytimg.com/vi/PHARBTwF89k/mqdefault.jpg)
i love u so much dawg
Much easier to understand than that CAST diagrams books and teachers always bang on about!
Also random question but where did the whole concept come from with sin , cos, tan? In the real world would you need ti use the graphs of these functions?
That was so helpful, thank you
Best Teacher ever, thank you so much.
11:46 hi jack, I know the angles in question are obtuse but when drawing the sin x graph why do you stay between 90 and 180?
Angles between 90 and 180 are obtuse?
because triangles cant be above 180 degrees and so it cant be above 180
Legend
Really helpful!
Ur my savior
thank you so much for this
inverse tan(x)=-43/6root66 gives me -43.41 on the calculator which is not an obtuse angle. I’m confused.
The calculator only gives you the solution between -90 degrees and 90 degrees when you use inverse tan. So you need to add 180 degrees to get the obtuse angle.
The proof of each trigonometric function shows that sin(x) is the value of the height of the triangle, the cosine(x) is the width and the tan(x) is the gradient. So when we are working out in this question the values of tan and cosine we input them into the ratio given by SohCahToa and not just simply out them as either the height, width or gradient? Can someone please expalin my confusion as i feel the two rules are contradictory. I feel it has somthing to do with the radius being the value of one in the proof example?
sin(x) is the height and cos(x) is the base of a right-angled triangle with angle x, IF the hypotenuse is of length 1. Otherwise, sin(x) = opp/hyp, cos(x) = adj/hyp as from SOHCAHTOA.
TLMaths Thank you! that’s so helpful
sir how would you do it if it said something like cos squared or sin squared or something
Well if you know sin(x)=1/4, for example, then sin^2(x)=(1/4)^2=1/16
I need to solve 2sin^3 x +3sin^2 x -8sinx+3 equals 0 and I’m unsure where to go. Help is much appreciated 👍🏼
Looks like a hidden cubic. Solve 2y^3 + 3y^2 - 8y + 3 = 0 to get y = -3, 1, 1/2
Then solve:
sin(x) = -3 (no solutions)
sin(x) = 1
sin(x) = 1/2
How 6 Sqrt root?? Is not it 65 squared times 43 then we put the result in sqrt?
a^2 + 43^2 = 65^2
a^2 = 65^2 - 43^2
a^2 = 2376
a = sqrt(2376) = 6*sqrt(66)
Hi, Sorry to bother you but please can you help me with this question, It would be highly appreciated.
Solve, for -180
tan(x-40) = 1.5
x-40 = arctan(1.5) = 56.30993247
x = 96.30993247
Then add/subtract 180 to this value to collect any other solutions.
x = 96.3... - 180 = -83.69006753
so x = {-83.7,96.3} to 1dp
@@TLMaths legend