Sin(28 degrees)squared + Cos(28 degrees)squared = ? TRIG students, NO Calculator!

Рет қаралды 7,248

Күн бұрын

Trigonometric Identities - an introduction.
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Пікірлер: 39

@tomtke7351 Жыл бұрын

This is a SNEAKY PROBLEM ... because EXPERIENCE teaches that sin^2 + cos^2 = 1. It's one of those things that comes about from lots of experience.. But a proof is cool too, right? For a right triangle and good ol' Pythagoras who came up with Pythagorean's Theorem: A^2 + B^2 = C^2 eq.1 and this is a must learn so just do it because it's as easy as A,B,C Then trigonometry says: sin (a) = A/C sin (a)^2 = A^2/C^2 cos (a) = B/C cos (b)^2 = B^2/C^2 so sin(a)^2+cos(a)^2 = A^2/C^2 + B^2/C^2 = (1/C^2)(A^2+B^2) eq.2 A^2 + B^2 = C^2 eq.1 (1/C^2)(A^2+B^2) = ? eq.2 eq.1 into eq.2 => (1/C^2)(C^2) = ? = 1 abbreviated : sin^2 + cos^2 = 1 sin^2(28°)+cos^2(28°)=1 sin^2(29°)+cos^2(29°)=1 sin^2(99°)+cos^2(99°)=1

@johnpaullogan1365 11 ай бұрын

draw your unit circle people. it's obvious sin(theta)^2+cos(theta)^2=1 for any theta. sin(theta) and cos(theta) are the two legs of a right triaangle with hypotenuse 1. and by pythagorean theorem we know that a^2+b^2=c^2

@russelllomando8460 Жыл бұрын

haven't used trig in 5+ decades. nice refresher. i kinda remember SOHCAHTOA.

@ECO473 Жыл бұрын

I haven't used it in five decades either, and won't use it in the next five. If one is not in STEM (and I'm not)...WHERE IS THIS RELEVANT???

@michallesz2 Ай бұрын

sin(x)=a/c , cos(x)=b/c => (a/c)^2 + ( b/c)^2 = (a^2+b^2)/c^2 => a^2+b^2=c^2 => c^2/c^2=1

@TheFallibleFiend Жыл бұрын

The sum of the squares of the legs of a right triangle whose hypotenuse is 1, because it's a unit circle.

@robertstuart6645 Жыл бұрын

This is one of the fundamental trigonometric identities. Very useful when integrating some trigonometric functions and expressions.

@norcalovenworks Жыл бұрын

1. I am an engineer. This is something that any engineer will know. This is just x**2 +y**2 on a unit circle. Kind of the definition of cos and sin.

@Michael43713 Жыл бұрын

Are your parentheses in the right place as in (sin28°)^2 rather than sin(28°)^2?

@johnspathonis1078 Жыл бұрын

I agree 100%.

@johnpaullogan1365 11 ай бұрын

@@johnspathonis1078 given it is a function sin^2(theta) certainly has no meaning. (sin(theta))^2 would probably be the least ambiguous but given these parentheses are denoting the aargument to a function rather than the way parentheses are usually used in math i don't think sin(theta)^2 is ambiguous really

@johnspathonis1078 11 ай бұрын

Can you reference an engineering maths book to support your argument?@@johnpaullogan1365

@whoff59 10 ай бұрын

I think sin (28°)² would be the value of "28⁰ squared" (convert to pi notation first) and then apply the sin function to the result. I really think it should be written like sin² (28°) or maybe (sin (28°))²

@brettbuck7362 4 ай бұрын

No, they are not. Its supposed to be sin^2(value), etc, to avoid this kind of confusion. A different nitpick is that the arguments of the sine function are supposed to be in radians.

@johnspathonis1078 Жыл бұрын

I agree with Michael43713 below. I think you have made a mistake. The actual probem set is sin 784 + cos 784. I believe you have the squared sign in the wrong place. My engineering maths books show that the squared sign should be placed immediately after the sin and cos term i.e sin^2(28) and cos^2(28). I normally would not have worried about this but you are very pedantic about getting maths absolutely correct ---Correct?

@donmoore7785 2 ай бұрын

Yes you are correct. He brags about his skills, but I have never seen what he claims verbally the problem to be to be written that way.

@jeffreydickson8888 9 ай бұрын

that identity is easily explained using a unit circle and the pythagorean theorem. not sure why this video didn't go down that road. thanks for your tutrials

@markcrites7060 2 ай бұрын

You missed out on explaining this in terms of the unit circle. It's a very clear way of showing why this is called the Pythagorean identity. If you think of sign as your y-coordinate on the unit circle and cosine as your X coordinate on the unit circle they form a triangle with the radius of the circle as the hypotenuse. Since the radius of the unit circle is 1, it becomes clear that sine squared plus cosine squared is equal to 1.

@franklemm6780 3 күн бұрын

Answer=1. Sin²(a)+cos²(b)=1

@tjwiets6691 Жыл бұрын

For an amazing visualization of trig functions and what the trig idendities, watch Beautiful Math channel's video "All 6 Trig Functions on the Unit Circle". It shows a wonderful visualization of the trig function relationships in a way I wish I could have seen 30+ yrs ago. At the time I was trying to memorize them but understanding the relationships as they're presented would have made it so much easier to learn them.

@richardvoogd705 9 ай бұрын

When i was in class many years ago I was taught sin²(angle)+cos²(angle)=1. I misread the thumbnail as sin(angle²)+cos (angle²)=1, which works differently. 😮

@Mrskateboardboy Жыл бұрын

Is the answer the hypotenuse squared?

@donmoore7785 2 ай бұрын

It looks like you squared the angles, not the sin and cos. What are those units - degrees squared? Why did you write it that way?

@imagseer 2 ай бұрын

1. Only because I remember it from school, but don't know why. This will be interesting

@olenfersoi8887 Жыл бұрын

I didn't remember this "identity" from decades ago...but I remembered what a sine & cosine are & filled in the Pythagoran ratio numbers & figured it out. Rather than rambling on endlessly about other identities, it would have been helpful if you thoroughly explain this ONE, and showed a triangle, the sine & cosine...illustrating the they represent the lengths of a triangles sides in relation to the hypotenuse, why that particular identity equaled one...thus, that the sum of those squares equals the hyp. squared. You said it was the Pythagorean Identity, but didn't explain why. Missed opportunnity. I appreciate your love of teaching...but sometimes you go off on a tangent (ha ha) rather than explaining one thin completely.

@ECO473 Жыл бұрын

Where would I ever use this in non math, non STEM working life???

@johnpaullogan1365 11 ай бұрын

it's basic application of pythagoren theorem. helped my contractor find whether a door would hit a vanity by proving it would need to be aa 38" door to hit it with how far from the wall the corner was just today using that

@ECO473 11 ай бұрын

@@johnpaullogan1365 You're a better man than I am, sir. I can respect that point.

@jeffreydickson8888 9 ай бұрын

a thorough understanding of at least the pythagorean theorem can simplify a lot of carpentry applications. Sometimes you know the lengths and can apply the formula directly, sometimes you know the angles and need to use the trig functions to find the lengths. Is it absolutely necessary/ probably not but it sure makes things easier.

@ECO473 Жыл бұрын

This only reminded me of why I failed trigonometry at my s**thole of a high school... twice...and why I haven't used it in forty-plus years of professional life since. What a waste...THEN AND NOW.