If cos degree equals to 0.8641
What is Sin degree?
I have no idea how to find this.
Please help me. I got help from two people, but I'm not getting the answer and how they got the numbers either.
Someone says:
cos^2+sin^2=1
sinDegree=sqrt(1-cos^2degree)
Another person says:
I recognize .8641 as an approximation to √3/2
if cos x = √3/2
x = 30°
sin30° = 1/2 or .5
using your .8641
sinx = .5033
Look. If cos(x) = 0.8641, you use your cos^-1 button to get x.
cos^-1(.8641) = 30.22°
sin 30.22° = 0.5033
So, since they gave you the answer in two different ways, as well as a sanity check to see why it makes sense, what is your work, which produces something else?
If you really have no idea, and cannot understand the answer when it is presented, you have some serious study to do.
Ok thank you. that makes more sense. I didn't understand the square root thing they did.
Simran, thanks for asking for me
To find the value of sin degree given that cos degree is 0.8641, you can use trigonometric identities or recognize the value as an approximation of a well-known trigonometric ratio. Here are two methods to calculate the answer:
Method 1:
1. Start with the trigonometric identity: cos^2 + sin^2 = 1.
2. Substitute the given value, cos degree = 0.8641, into the equation: 0.8641^2 + sin^2 = 1.
3. Rearrange the equation to solve for sin^2: sin^2 = 1 - 0.8641^2.
4. Calculate sin^2 by subtracting 0.8641^2 from 1.
5. Take the square root of sin^2 to find sin degree:
sin degree = sqrt(1 - 0.8641^2).
Method 2:
1. Recognize 0.8641 as an approximation of √3/2.
2. Recall the values of cosine and sine for the commonly used angles on the unit circle.
For example, cos 30° = √3/2 and sin 30° = 1/2.
3. Since cos degree = 0.8641 is close to √3/2, we can infer that the angle is approximately 30°.
4. Use the known value of sin 30° to find sin degree:
sin degree ≈ sin 30° = 1/2.
Both methods should give you an answer for sin degree. However, the first method provides a more precise calculation by using the trigonometric identity. The second method is based on recognizing the approximation and using the known value for 30°.