Finding Value of Angle for Trigonometric Function

Finding any value of any angle for trigonometric function |
The finding of values of sin x and cos x is time taking as it involves calculations in roots and decimal but can be handy in exams where you are allowed to carry simple calculators.
Before doing so you need to learn following values.

Value of Angle for Trigonometric Function

Step 1) If you have to find value of sin x or cos x then write it in following form
Sin x = sin (a+b) (i) Or cos x = cos (a+b) (ii) respectively.
Where a is angle whose sin and cos value you know and b is obviously x-a.

Step 2) Select the Appropriate formula
Formula to be used :-

1) Sin x = sin (a+b) = sin a + cos a (bπ/180)
2) Cos x = cos (a+b) = cos a – sin a (bπ/180)

*Since the formula tends to lose it accuracy as |b|>10. So ‘a’ should be chosen very wisely.

Example 1: Find sin 50

Sin 50 then a=45 and b=5
So equation (i) for sin 50 becomes sin50 = sin (45+5)

Now using the formula for sin

Sin 50 = sin (45+5) = sin 45 + (cos 45 x 5π/180)
=1/sqrt(2) + (1/sqrt(2) x 5π/180)

True value is 0.766.

Example 2: Find sin 10

Step 1) Sin 10=sin ( 15+ (-5) )
Step 2) Using the formula
Sin 10=sin ( 15+ (-5) ) = sin 15 + (cos 15 x (-5π/180))
=1/4 + (24/25 x (-5π/180))
= 0.166

True value 0.173.

There is 4% inaccuracy in above answer due to the fact that the value of sin 15 used i.e, 1\4 is an approx. value for easy memorization.

*tan x, sec x, cosec x and cot x can be found using values of sin x and cos x and using basic trigonometric identities.

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