I have to answer these equations but I don't know how to?

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2 Answers
May 2, 2018

tan(-x)=-0.5
sin(-x)=-0.7
cos(-x)=0.2
tan(pi+x)=-4

Explanation:

Tangent and Sine are odd functions. In any odd function, f(-x)=-f(x). Applying this to tangent, tan(-x)=-tan(x), so if tan(x)=0.5, tan(-x)=-0.5. The same process yields us sin(-x)=-0.7.

Cosine is an even function. In an even function, f(-x)=f(x). In other words, cos(-x)=cos(x). If cos(x)=0.2, cos(-x)=0.2.

Tangent is a function with a period of pi. Therefore, every pi, tangent will be the same number. As such, tan(pi+x)=tan(x), so tan(x)=-4

May 2, 2018

If tan x = .5 then tan(-x)=-tan x = -.5

If sin x = .7 then sin(-x) = -sin x =- .7

If cos x = .2 then cos(-x) = cos x = .2

If tan x = -4 then tan(pi+x)=tan x= -4

Explanation:

These are asking the basic question of what happens to a trig function when we negate its argument. Negating an angle means reflecting it in the x axis. This flips the sign of the sine, but leaves the cosine alone. So,

cos (-x) = cos x

sin(-x) = -sin x

tan (-x) = {sin(-x)}/{cos(-x)} = -tan (x)

When we add pi to an angle we flip the sign on both sine and cosine.

cos(x + \pi) = - cos x

sin(x + \pi) = - sin x

tan(x+ \pi) = {cos(x+pi)}/{sin(x+pi)} = tan x

With that as background, let's do the questions:

If tan x = .5 then tan(-x)=-tan x = -.5

If sin x = .7 then sin(-x) = -sin x =- .7

If cos x = .2 then cos(-x) = cos x = .2

If tan x = -4 then tan(pi+x)=tan x= -4