Question

Find tan 0 for each value of 0Try these C-D

Answer 1

We have to find the value of the tangent function for these angles:

a. θ = 300°

`\begin{gathered} \tan (300\degree)=\tan (300\cdot(\pi)/(180))=\tan ((10)/(6)\pi)=\tan ((4)/(6)\pi+(6)/(6)\pi)=\tan ((2\pi)/(3)) \\ \tan ((2\pi)/(3))=(\sin((2\pi)/(3)))/(\cos((2\pi)/(3)))=\frac{\frac{\sqrt[]{3}}{2}}{-(1)/(2)}=-\sqrt[]{3} \end{gathered}`

b. θ = 450°

c. θ = 2π/3 = 300°

`\tan ((2\pi)/(3))=-\sqrt[]{3}`

d. θ = 11π/4

`\begin{gathered} \tan ((11\pi)/(4))=\tan ((3\pi)/(4)+2\pi)=\tan ((3\pi)/(4)) \\ \tan ((3\pi)/(4))=(\sin((3\pi)/(4)))/(\cos((3\pi)/(4)))=\frac{\frac{\sqrt[]{2}}{2}}{-\frac{\sqrt[]{2}}{2}}=-1 \end{gathered}`

Answer:

a. -√3

b. Undefined

c. -√3

d. -1