Sin 90 =
- Infinity
- 0
- 1
Explanation
Sine reaches its maximum value at 90 degrees, where sin 90 = 1. This is the peak of the sine curve, corresponding to the opposite side equalling the hypotenuse. Sin 0 is 0 and the sine function never reaches infinity, so the other options are incorrect.
bennguli asking:
how to find a sine of an angle without a calculator or mathematical table?somebody assist please
Community Comments (3)
D
dimky Posts: 514 12.04.2017 / 17:43
You have to remember this.
J
JD2016 Posts: 54 13.04.2017 / 00:15
Like DIMKY says you have to remember it but it's all based on the "unit circle". This is easier to explain with a diagram but you take a circle of radius 1 unit centred on co-ordinates 0,0. The X and Y axes divide the unit circle into 4 quadrants. The first quadrant is the top right. Draw a radius (of length 1 unit) at any angle to the x axis (horizontal) in the first quadrant. Call the angle "A". Sine A and Cosine A are the coordinates of the point where the radius intersects or meets the circle. The Y coordinate of that point is Sin A and the X coordinate is Cos A.
So if the angle is 90 degrees, the radius is vertical and lies along the Y axis. The intersection of the radius and the circle is the point (0,1) - i.e out 0 units along the X axis and up 1 unit on the Y axis. Therefore Cos 0 = 0 and Sin 0 =1.
Once you can visualise the unit circle, the radius and the angle it makes with the X axis, you can work out the Sine and Cosine of any angle.
Take 45 degrees. In that case you have a radius ( of length 1 unit) drawn at the same angle to the X and Y axis - i.e. it splits that quadrant into 2 equal halves.
Sin 45 will be the vertical distance from the point of intersection of the radius and the circle, to the X axis. Call it Y. But since we're talking about 45 degrees, the horizontal and vertical distances are the same, so it forms a triangle with hypotenuse (the long side) equal to the radius (=1)and the other 2 sides are = Y (or X). So using Pythagoras Theorem - 1 Squared = Y squared + Y squared.
1 squared = 2 Y squared
1/2 = Y squared
Y = 1 /square root of 2 = 1/1.414 = 0.707 which is the number you get from tables or from a calculator when you press the button for Sin 45.
So if the angle is 90 degrees, the radius is vertical and lies along the Y axis. The intersection of the radius and the circle is the point (0,1) - i.e out 0 units along the X axis and up 1 unit on the Y axis. Therefore Cos 0 = 0 and Sin 0 =1.
Once you can visualise the unit circle, the radius and the angle it makes with the X axis, you can work out the Sine and Cosine of any angle.
Take 45 degrees. In that case you have a radius ( of length 1 unit) drawn at the same angle to the X and Y axis - i.e. it splits that quadrant into 2 equal halves.
Sin 45 will be the vertical distance from the point of intersection of the radius and the circle, to the X axis. Call it Y. But since we're talking about 45 degrees, the horizontal and vertical distances are the same, so it forms a triangle with hypotenuse (the long side) equal to the radius (=1)and the other 2 sides are = Y (or X). So using Pythagoras Theorem - 1 Squared = Y squared + Y squared.
1 squared = 2 Y squared
1/2 = Y squared
Y = 1 /square root of 2 = 1/1.414 = 0.707 which is the number you get from tables or from a calculator when you press the button for Sin 45.
B
bennguli Posts: 2 13.04.2017 / 11:50
very helpful thanks alot
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