# How to find out the sin value from cos

In summary, the conversation discusses solving for unknown values in trigonometric equations and using a geometrical approach to find values of sine and cosine. The use of trigonometric tables is not necessary and the exact answer may involve a surd, which is a square root symbol. The approximate answer can be rounded to a certain number of decimal places. The conversation also mentions the concept of a "conjugate surd," which may refer to a heavy metal band from Manchester in the 1970s.
Homework Statement
we know α ∈ [0, π] and cos α = √5/3, what is the exact value of sin α and the approx. angle of sin α?
Relevant Equations
sin[sup]2[/sup] α + cos[sup]2[/sup] α = 1, unit circle
First off sorry if something doesn't make sense, english is not my native language.

I know i should start with sin2 α + cos2 = 1, but ant really continue from it.
i am being confused by cos α = √5/3 since i know it isn't found in normal trig tables. So my problem is how to find out values of any radian value, and how to find out the corresponding value in sin?

I am not sure where your problem is. You do not need trigonometric tables because you are already given the value of the cosine of the angle and you have the trigonometric one, which includes the sine of the angle and the cosine of the angle. One known and one unknown. Solve for the unknown.

topsquark
I am also not clear what your problem is. But a geometrical approach would be to sketch a right-angled triangle with one of its angles ##\alpha##.

With appropriate sides of lengths ##\sqrt 5## and ##3##, you have ##\cos {\alpha} = \frac {\sqrt 5}3##. And take it from there.

Edit: The exact answer might (or might not) include a surd (square root).

The approximate answer should be the exact answer rounded to, say, 3 decimal places.

topsquark
Steve4Physics said:
I am also not clear what your problem is. But a geometrical approach would be to sketch a right-angled triangle with one of its angles ##\alpha##.

With appropriate sides of lengths ##\sqrt 5## and ##3##, you have ##\cos {\alpha} = \frac {\sqrt 5}3##. And take it from there.

Edit: The exact answer might (or might not) include a surd (square root).

The approximate answer should be the exact answer rounded to, say, 3 decimal places.
i need the square root for sin(x)2=4/9, i may have overestimated the question at first

i need the square root for sin(x)2=4/9, i may have overestimated the question at first
You don't need a square root symbol in your exact answer because (of course) ##\frac 49## has an exact rational square root.

But if the question had said (for example) ##\cos \alpha = \frac {\sqrt 7}3##, then your exact answer would require a square root symbol.

Steve4Physics said:
surd
TIL.

(almost six decades on the planet - my first encounter)

DaveC426913 said:
TIL.
More than seven decades on the planet - and my first encounter!

Have you ever heard of the "conjugate surd" ?

would that be the "turd" ?

malawi_glenn
SammyS said:
Have you ever heard of the "conjugate surd" ?
I believe they were a heavy metal band from Manchester, back in the early 1970s.

malawi_glenn and berkeman

## 1. How do I find the sin value from the cos?

The sin value can be found by using the trigonometric identity: sin^2(x) + cos^2(x) = 1. Rearranging this equation, we get sin^2(x) = 1 - cos^2(x). Taking the square root of both sides, we get sin(x) = ±√(1 - cos^2(x)). Depending on the quadrant of the angle, we can determine the sign of the sin value.

## 2. Can I use a calculator to find the sin value from the cos?

Yes, most scientific calculators have a function for finding the sin value from the cos. Look for a "sin^-1" or "arcsin" button on your calculator. Simply enter the cos value and press the appropriate button to get the sin value.

## 3. Is there a specific formula for finding the sin value from the cos?

Yes, the formula is sin(x) = ±√(1 - cos^2(x)), as mentioned in the first question. This formula is derived from the Pythagorean identity and can be used to find the sin value for any angle.

## 4. How can I remember the formula for finding the sin value from the cos?

A helpful mnemonic for remembering this formula is "Some Old Hippie Caught Another Hippie Tripping On Acid." The first letter of each word corresponds to the first letter of the terms in the formula: sin = √(1 - cos^2).

## 5. Can I use the same formula to find the cos value from the sin?

Yes, the same formula can be used to find the cos value from the sin. Simply rearrange the formula to cos(x) = ±√(1 - sin^2(x)). Again, the sign of the cos value will depend on the quadrant of the angle.

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