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Answer: sin(θ)
Sin Calculator is used to calculate the sine of a given angle. You can specify the angle in degrees or radians. The Sin Calculator computes the sine of given angle and provides a step by step solution.
How to calculate sin(θ) using graph?
Step 1 - Draw unit circle
Draw a unit circle with \(O(0, 0)\) as the center of the circle on the graph paper.
Step 2 - Draw line with angle θ
Draw a line from center of the circle making an angle θ with X-axis, using a protractor.
Mark the point as \(P\), where the line touches the circle.
Step 3 - Form Right Angle Triangle PQO
Draw a perpendicular line from \(P\) to the X-axis.
Mark the point as \(Q\), where the perpendicular line touches the X-axis.
Now, we have a triangle, PQO with right angle at \(Q\), \(∠POQ = θ\), and \(OP = 1\) unit.
Step 4 - Calculate sin(θ)
In a right angled triangle, Sine of an angle (θ) is the ratio of the length of the opposite side to the length of the hypotenuse.
The formula for sin(θ) is:
sin(θ) == (Length of Opposite side) / (Length of Hypotenuse)
From triangle PQO,
sin(θ) == PQ/OP
Since we have taken a unit circle, and the hypotenuse (OP) is equal the radius of the circle which is 1 unit
sin(θ) == PQ/1
sin(θ) == PQ
Measure the length \(PQ\) on the graph and that length is the value of sin(θ).
Note: If you have drawn a bigger circle on the graph, with a radius other than 1 unit, then divide the length of \(PQ\) with the radius of the circle to get the \(sin(θ)\) value. For example, if you have considered 10cm as radius of the circle on the graph, then \(PQ\) should be divided with 10cm to get \(sin(θ)\) value.