hw: practice for test 2 : chapter 6 due before 2pm score: 13/19 answered: 13/19 question 8 fill in the…

hw: practice for test 2 : chapter 6 due before 2pm score: 13/19 answered: 13/19 question 8 fill in the blanks: 1. if tan x = -4 then tan(-x) = 2. if sin x = 0.3 then sin(-x) = 3. if cos x = 0.8 then cos(-x)= 4. if tan x = 2.5 then tan(π + x)= question help: worked example 1 message instructor submit question

hw: practice for test 2 : chapter 6 due before 2pm score: 13/19 answered: 13/19 question 8 fill in the blanks: 1. if tan x = -4 then tan(-x) = 2. if sin x = 0.3 then sin(-x) = 3. if cos x = 0.8 then cos(-x)= 4. if tan x = 2.5 then tan(π + x)= question help: worked example 1 message instructor submit question

Answer

Explanation:

Step1: Recall tangent - odd function property

The tangent function is odd, i.e., $\tan(-x)=-\tan(x)$. Given $\tan(x)= - 4$, then $\tan(-x)=-(-4) = 4$.

Step2: Recall sine - odd function property

The sine function is odd, i.e., $\sin(-x)=-\sin(x)$. Given $\sin(x)=0.3$, then $\sin(-x)=- 0.3$.

Step3: Recall cosine - even function property

The cosine function is even, i.e., $\cos(-x)=\cos(x)$. Given $\cos(x)=0.8$, then $\cos(-x)=0.8$.

Step4: Recall tangent - periodicity property

The tangent function has a period of $\pi$, i.e., $\tan(x + \pi)=\tan(x)$. Given $\tan(x)=2.5$, then $\tan(x+\pi)=2.5$.

Answer:

  1. 4
  2. -0.3
  3. 0.8
  4. 2.5