Question

negative angle identities

1. if \\( \tan \theta = 3.1 \\), then \\( \tan (-\theta)=? \\)
2. if \\( \cos \theta=-0.25 \\) \\( \theta)=? \\)

\\( \sin (-\theta)=-\sin \theta \quad \csc (-\theta)=-\csc \theta \\)
\\( \cos (-\theta)=\cos \theta \quad \sec (-\theta)=\sec \theta \\)
\\( \tan (-\theta)=-\tan \theta \quad \cot (-\theta)=-\cot \theta \\)
fill in the blanks:

1. if \\( \tan x = 2 \\) then \\( \tan (-x)= \\)
2. if \\( \sin x = 0.4 \\) then \\( \sin (-x)= \\)
3. if \\( \cos x = 0.3 \\) then \\( \cos (-x)= \\)
4. if \\( \tan x = 2 \\) then \\( \tan (\pi + x)= \\)

question help: worked example 1

Explanation:

Step1: Use trigonometric identities

For tangent function, \(\tan(-x)=-\tan x\). Given \(\tan x = 2\), so \(\tan(-x)=- 2\).
For sine function, \(\sin(-x)=-\sin x\). Given \(\sin x=0.4\), so \(\sin(-x)=-0.4\).
For cosine function, \(\cos(-x)=\cos x\). Given \(\cos x = 0.3\), so \(\cos(-x)=0.3\).
For tangent function, \(\tan(\pi + x)=\tan x\) (because tangent has a period of \(\pi\)). Given \(\tan x=2\), so \(\tan(\pi + x)=2\).

Answer:

1. \(-2\)
2. \(-0.4\)
3. \(0.3\)
4. \(2\)