Q: Is there a specific value of sin, cos or tan or are they just like a placeholder with different values each time like x,y,z? Basically speaking, does sin have a specific value when it is 100%?

sin(x), cos(x) and tan(x) are functions, so their value depends on what value of x you input. Sure, you can use different variables (like sin(z) or tan(m)) but "sin", "cos" and "tan" by themselves have no meaning.

Q: I don't get how side opposite of the 30-degree angle is x/2. can someone help me understand this problem.

When you divide an equilateral triangle into two, you have two 30-60-90 triangles of equal length. The opposite side of the 30 degree angle is the base. When you split the base of an equilateral triangle of side length x into 2, you get x/2. You can also try drawing it out. Hope this helps

Q: In the second video, when Khan does the princibe root of sqrt2x^2 and c^2, how come the x goes outside and the two is left in?

Its simple mathematics, think of this in this way: 2*x*x = c*c we see 'x' and 'c' to be squared i.e. 2*x^2 = c^2 If you recall studying 'Real Numbers' or 'Indices', you would know that the root of 'x^2' is 'x' , the root of 'c^2' is 'c' and of '2' is '(root sign)2'. So by simply finding root of both side: 2*x^2 = c^2, will be (root)2*x = c and so we write it as : x*(root)2 = c, and so here comes the concept that 2 is left behind, when truly it is not.

Q: I don't get how you're getting these answers, the math does not make sense. How is the Tan(30) not 1/√3 . I don't understand how you go from 1/√3 to √3/3. Same with Sin(45), how does he get √2/2? What am I missing here?

you have to rationalize the denominator. to rationalize 1/sqrt(3), you want to have no square root in the denominator, so you multiply numerator and denominator by sqrt(3): 1/sqrt(3)*sqrt(3)/sqrt(3)=sqrt(3)/(sqrt(3)*sqrt(3)). sqrt(3)*sqrt(3)=3, so you get sqrt(3)/3. 1/sqrt(3) is equal to sqrt(3)/3, but they're just written differently because sqrt(3)/3 is considered simpler. same goes to the sqrt(2)/2

Q: this is related to tan 60 and was a multiple-choice question in one of my papers; the angle made by the line x/3 - y/2 = 1 with the positive direction of the x-axis is closest to: then it gave some options, the correct answer being 33 degrees. how do I get to that answer? I know that the gradient of the line is 2/3 and so the angle made by the line with the positive direction of the x-axis will be: angle= tan-1 (inverse of tan) 2/3. but how does this become close to 33 degrees? I appreciate any help and thanks so much!

One of the options given is closest to the true measure of the angle. That option is your answer.

Q: When I did math for cos60 I got 1 over square root of 2. The check said it was correct, but the table has square root of 2 over 2. Why the discrepancy? Same for tan30. I got 1 over square root of 3, but the chart says square root of 3 over 3.

Because many tests require people to have a rational denominator, so we move the square root into the numerator.

Question 1

Can these trigonometric rations of special triangles be used for finding the trigonometric ratios for other angles like 50 degrees? For example, if I did sin60 * 5/6, would that equal to sin50?

Accepted Answer

No. The trig functions are not linear; therefore, you cannot use ratios like that.

Question 2

why does sal specify that tangent of 30 degrees is √3/3 ? isn't it 1/√3

Accepted Answer

You are right but, we don't like to have the square roots on the bottom so we multiply both sides by the square root

Question 3

what are the sin, cos and tan of 90 degrees?

Accepted Answer

You can't really have a tangent of 90 degrees, at least when it comes to reference triangles, because that would indicate two 90 degree angles. As Sal mentioned in the videos talking about the Unit Circle, you can't have two 90 degree angles in a Triangle. You could theoretically have < or = 89.9999_` triangle, but theoretically two 90.00* = a line.

Question 4

Is there a specific value of sin, cos or tan or are they just like a placeholder with different values each time like x,y,z?
Basically speaking, does sin have a specific value when it is 100%?

Accepted Answer

sin(x), cos(x) and tan(x) are functions, so their value depends on what value of x you input. Sure, you can use different variables (like sin(z) or tan(m)) but "sin", "cos" and "tan" by themselves have no meaning.

Question 5

I don't get how side opposite of the 30-degree angle is x/2. can someone help me understand this problem.

Accepted Answer

When you divide an equilateral triangle into two, you have two 30-60-90 triangles of equal length. The opposite side of the 30 degree angle is the base. When you split the base of an equilateral triangle of side length x into 2, you get x/2. You can also try drawing it out.
Hope this helps

Question 6

In the second video, when Khan does the princibe root of sqrt2x^2 and c^2, how come the x goes outside and the two is left in?

Accepted Answer

Its simple mathematics, think of this in this way:
2*x*x = c*c
we see 'x' and 'c' to be squared i.e.
2*x^2 = c^2
If you recall studying 'Real Numbers' or 'Indices', you would know that the root of 'x^2' is 'x' ,  the root of 'c^2' is 'c' and of '2' is '(root sign)2'.
So by simply finding root of both side:
2*x^2 = c^2, will be
(root)2*x = c
and so we write it as :
x*(root)2 = c,
and so here comes the concept that 2 is left behind, when truly it is not.

Question 7

I don't get how you're getting these answers, the math does not make sense. How is the Tan(30) not 1/√3 . I don't understand how you go from 1/√3  to √3/3. Same with Sin(45), how does he get √2/2? What am I missing here?

Accepted Answer

you have to rationalize the denominator.
to rationalize 1/sqrt(3), you want to have no square root in the denominator, so you multiply numerator and denominator by sqrt(3): 1/sqrt(3)*sqrt(3)/sqrt(3)=sqrt(3)/(sqrt(3)*sqrt(3)).
sqrt(3)*sqrt(3)=3, so you get sqrt(3)/3.
1/sqrt(3) is equal to sqrt(3)/3, but they're just written differently because sqrt(3)/3 is considered simpler.
same goes to the sqrt(2)/2

Question 8

this is related to tan 60 and was a multiple-choice question in one of my papers;
  
the angle made by the line x/3 - y/2 = 1 with the positive direction of the x-axis is closest to:

then it gave some options, the correct answer being 33 degrees.

how do I get to that answer? I know that the gradient of the line is 2/3 and so the angle made by the line with the positive direction of the x-axis will be:

angle= tan-1 (inverse of tan) 2/3. 
 
but how does this become close to 33 degrees?

I appreciate any help and thanks so much!

Accepted Answer

One of the options given is closest to the true measure of the angle.
That option is your answer.

Question 9

When I did math for cos60 I got 1 over square root of 2. The check said it was correct, but the table has square root of 2 over 2. Why the discrepancy? Same for tan30. I got 1 over square root of 3, but the chart says square root of 3 over 3.

Accepted Answer

Because many tests require people to have a rational denominator, so we move the square root into the numerator.

	$\cos (θ)$ ‍	$\sin (θ)$ ‍	$\tan (θ)$ ‍
$θ = 30^{\circ}$ ‍	$\frac{\sqrt{3}}{2}$ ‍	$\frac{1}{2}$ ‍	$\frac{\sqrt{3}}{3} = \frac{1}{\sqrt{3}}$ ‍
$θ = 45^{\circ}$ ‍	$\frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$ ‍	$\frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$ ‍	$1$ ‍
$θ = 60^{\circ}$ ‍	$\frac{1}{2}$ ‍	$\frac{\sqrt{3}}{2}$ ‍	$\sqrt{3}$ ‍

Trigonometry

Course: Trigonometry > Unit 1

Trig ratios of special triangles

The special triangles

The trigonometric ratios of $30^{\circ}$ ‍

What is $\sin (30^{\circ})$ ‍?

What is $\cos (30^{\circ})$ ‍?

What is $\tan (30^{\circ})$ ‍?

The trigonometric ratios of $45^{\circ}$ ‍

What is $\cos (45^{\circ})$ ‍?

What is $\sin (45^{\circ})$ ‍?

What is $\tan (45^{\circ})$ ‍?

The trigonometric ratios of 60 $^{\circ}$ ‍

What is $\cos (60^{\circ})$ ‍?

What is $\sin (60^{\circ})$ ‍?

What is $\tan (60^{\circ})$ ‍?

A summary

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Trigonometry

Course: Trigonometry > Unit 1

The special triangles

The trigonometric ratios of 30∘‍

What is sin⁡(30∘)‍ ?

What is cos⁡(30∘)‍ ?

What is tan⁡(30∘)‍ ?

The trigonometric ratios of 45∘‍

What is cos⁡(45∘)‍ ?

What is sin⁡(45∘)‍ ?

What is tan⁡(45∘)‍ ?

The trigonometric ratios of 60∘‍

What is cos⁡(60∘)‍ ?

What is sin⁡(60∘)‍ ?

What is tan⁡(60∘)‍ ?