prove sin 30°= 1/2
thanks
Answers
Answered by
2
Hey,
As you know ,
Sin 30°=1/2 .
Replace the value in the above equation.
➡️1/2=1/2.
Hope it will help you.
Happy to help you.
@M.S.V.
As you know ,
Sin 30°=1/2 .
Replace the value in the above equation.
➡️1/2=1/2.
Hope it will help you.
Happy to help you.
@M.S.V.
saivivek16:
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Answered by
5
In the simplest of terms - Sine of an angle (in a right angled triangle) is the ratio of the side length of the side present opposite to the angle in question, to the length of the hypotenuse (the longest side and also the side opposite to the right angle itself)

To prove that sin 30 = 1/2, you could literally construct a right angled triangle ABC. The crudest method is -
Draw an arbitrarily long line.
Mark any point named A on it and use a Protractor to mark of 30 degrees from A and draw another long line.
Mark a point C on the initial line that you drew and again, use the protractor to draw a line that is 90 degrees to AC. Extend the 30 degree line from A and the 90 degree line from C until they meet. Let the point of intersection be B
Measure the ratio of BC/AB and it will be 0.5 or 1/2.
Another fun method is using a circle to calculate the same. For ease of construction, let us use a regular graph paper and a circle of radius 1 (you can mark off each unit in the graph as 0.2)
Draw a circle with radius 1 (so basically 5 units of the graph).
From the centre, mark off a 30 degree line to the X axis. Basically make a sector on the circle between the X axis and a 30 degree angle.
Draw a perpendicular to the X axis from the point where this 30 degree line touches the circle. Also draw a perpendicular to the Y axis (or a line parallel to the X axis) from this point.
You will see that the length of the line along the Y axis is 0.5 or basically the value of sine 30. The length of the line along the X axis will give you the value of cosine 30.

By Webysther - Own work, CC BY-SA 4.0, File:Webysther 20160305 - Ciclo trigonométrico.svg
The construction above can be used to show how sine and cosine of angles work. NI our case the calue of Theta will be 30.
If you would also like to know how sine waves and cosine waves (in electronics) work, then the following GIF would give you an idea
I SEARCHED IN NET
HOPE THIS HELPS YOU

To prove that sin 30 = 1/2, you could literally construct a right angled triangle ABC. The crudest method is -
Draw an arbitrarily long line.
Mark any point named A on it and use a Protractor to mark of 30 degrees from A and draw another long line.
Mark a point C on the initial line that you drew and again, use the protractor to draw a line that is 90 degrees to AC. Extend the 30 degree line from A and the 90 degree line from C until they meet. Let the point of intersection be B
Measure the ratio of BC/AB and it will be 0.5 or 1/2.
Another fun method is using a circle to calculate the same. For ease of construction, let us use a regular graph paper and a circle of radius 1 (you can mark off each unit in the graph as 0.2)
Draw a circle with radius 1 (so basically 5 units of the graph).
From the centre, mark off a 30 degree line to the X axis. Basically make a sector on the circle between the X axis and a 30 degree angle.
Draw a perpendicular to the X axis from the point where this 30 degree line touches the circle. Also draw a perpendicular to the Y axis (or a line parallel to the X axis) from this point.
You will see that the length of the line along the Y axis is 0.5 or basically the value of sine 30. The length of the line along the X axis will give you the value of cosine 30.

By Webysther - Own work, CC BY-SA 4.0, File:Webysther 20160305 - Ciclo trigonométrico.svg
The construction above can be used to show how sine and cosine of angles work. NI our case the calue of Theta will be 30.
If you would also like to know how sine waves and cosine waves (in electronics) work, then the following GIF would give you an idea
I SEARCHED IN NET
HOPE THIS HELPS YOU
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