Question

practice assignment 9.1 solving trigonometric equations with identities
score: 5/9 answered: 5/9
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question 6
fill in the blanks:

1. if \\( \tan x = - 3 \\) then \\( \tan ( - x ) = \\)
2. if \\( \sin x = 0.6 \\) then \\( \sin ( - x ) = \\)
3. if \\( \cos x = 0.9 \\) then \\( \cos ( - x ) = \\)
4. if \\( \tan x = 1 \\) then \\( \tan ( \pi + x ) = \\)

question help: worked example 1

Explanation:

Step1: Recall the property of tangent function

The tangent function is odd, i.e., \(\tan(-x)=-\tan x\). Given \(\tan x = - 3\), then \(\tan(-x)=-(-3)=3\).

Step2: Recall the property of sine function

The sine function is odd, i.e., \(\sin(-x)=-\sin x\). Given \(\sin x = 0.6\), then \(\sin(-x)=-0.6\).

Step3: Recall the property of cosine function

The cosine function is even, i.e., \(\cos(-x)=\cos x\). Given \(\cos x = 0.9\), then \(\cos(-x)=0.9\).

Step4: Recall the periodicity of tangent function

The tangent function has a period of \(\pi\), i.e., \(\tan(x + n\pi)=\tan x\) for any integer \(n\). Given \(\tan x = 1\) and \(n = 1\), then \(\tan(\pi + x)=\tan x=1\).

Answer:

1. \(3\)
2. \(-0.6\)
3. \(0.9\)
4. \(1\)