(please help) how to find tan 40° easily without calculator
Answers
Answer:here is your answer,
Yes, You can find the value of tan 40 without using calculator.
You can use Maclaurin Series, to find the value.
tan(x) = x+(1/3)3+(2/15)x5+(17/315)x7+....
Here, x should be in radians.
Given:
Degree = 40 = 0.698 = 0.7 apprx (1 Degree = 0.0174533 Radians)
tan(40) = 0.7 +(1/3)(0.7)3+(2/15)(0.7)5+(17/315)(0.7)7+....
= 0.7 + 0.1143 + 0.0224 + 0.004
tan(40) = 0.84 approx
Explanation:
Answer:
As we know, tan x = sin x/cos x
one way to find is using the values of sin 40 and cos 40.
or you can use the trignometric results:
similarly, using second formula:
tan (30 + 10) = tan 30 + tan 10 / (1-tan 30 tan 10)
tan 40 = 0.57735 + 0.176326 / ( 1-0.1018) ——→ values are approximated
= 0.753676/0.8982
tan 40 = 0.839095 —-> value of tan 40 by formula.
value by calculator = 0.8390996
They are very nearly equal.
Explanation: