All Sin Tan Cos Rule In Trigonometry
All Sin Tan Cos rule in trigonometry is a very simple but powerful method of finding out the value of various angles whose values are generally not known. With the application of all sin tan cos rule, it is possible to reduce larger angles to less than 90 degree. Now let’s jump right into the rule and learn it
In order to grasp the concept of the rule, one should have the knowledge of Cartesian co-ordinates. As it is known to all that Cartesian co ordinate system has got 4 quadrants which is widely used for plotting related variables to find out their correlation. For the All Sin Tan Cos Rule 4 quadrants are used for allocation like the figure below.
As the above figure indicates any value of trigonometric angle is considered to be positive (+Ve) in the first quadrant. And as shown in the figure above in the 2nd quadrant Sin is Positive, in third quadrant Tan is positive and in the 4th quadrant Cos is considered as positive.
Now lets say, it is asked to find out the value of Sin150°
We can write it as either Sin (90°+60°) or Sin (90°X2-30°)
Now lets allocate the angle in the quadrants. It will look like,
One thing here is to be kept in mind that all the angle starts from positive x axis towards the positive Y axis i.e anticlockwise. Now lets concentrate on the problem which is finding out of the value of Sin 150°.
If we consider Sin (90°+60°), we are reaching on 2nd quadrant where Sin is positive so the value of the angle is positive. Now one thing is to be seen is the how many multiple of 90° is considered. Here in the example it’s one multiple of 90° which is odd. In this case the complementary angle of sin will come and then the angle 60°. So Sin (90°+60°) can be written as cos60° i.e 0.5
And if we write Sin150°as Sin (90°X2-30°), we are again reaching in the 2nd quadrant where sin is positive and as the multiple of 90 degree is 2 (Even) in this case no change of the operator is required. So this angle can be reduced to Sin 30° whose value is also 0.5. So either way the value will be same.
Similarly any angle can be reduced for convenience of calculation.
Bonus Tip: If it is asked to find out the value of Cosec, Sec or Cot of a angle more than 90 degree, just find out the sin, cos and tan of the same angle respectively and then take the reciprocal of the same.
