Simplify and write the trigonometric expression in terms of sine and cosine: f(a
ID: 3026803 • Letter: S
Question
Simplify and write the trigonometric expression in terms of sine and cosine: f(a) f(E)- This is attempt 1 of 10 Evaluate the ollowing exspressions Your answer must beameact amgle in madians and in the interval - 7 . Example: Etrfor (a) tan-1(1)- b) tan-1(4)-Preview () tan3) This is attempt 1 of 10. fy to an expression involving a single trigonometric function with no fractions cos( - )+tan( )in) Preview This is attempt 1 of 10. linda simplified expression for tan(cos-G)) Question 5. Points possible: 5 This is attempt 1 of 10.Explanation / Answer
cot ( -x ) cos ( -x ) + sin ( -x )
cot (-x) = - cot x
cos (-x) = cos x
sin (-x) = - sin x
cot x = cos x / sin x
so we can write
cot ( -x ) cos ( -x ) + sin ( -x ) = - cos x / sin x * cos x - sin x
= - cos^2 x / sin x - sin x
= - cos^2 x - sin^2x / sin x
= - ( cos^2 x + sin^2 x ) / sin x
= -1 / sin x
hence, f(x) = sin x
2 a) tan^-1 (1) = pi/4
b) tan^-1 ( sqrt 3 / 3 ) = pi/6
c) tan^-1 ( - sqrt 3 /3 ) = - pi/6
3) cos ( -x ) + tan (-x) sin ( -x )
cos (-x) = cos x
tan (-x) =- tan x
sin (-x) = - sin x
cos ( -x ) + tan (-x) sin ( -x ) = cos x - sin x / cos x * - sin x
= cos x + sin^2 x / cos x
= cos^2 x + sin^2 x / cos x
= 1 / cos x
= sec x