Question

Does anyone know how to solve this? I don't know how to type it out so Im gonna attach a pic

Answer 1

Sin (theta)=
`- ( √(2) )/(2)`

Tan ( theta)=
`- 1`

Explanation:

`cos \: \: theta \: = ( √(2) )/(2) = (1)/( √(2) ) = cos \: (\pi)/(4 )`

`cos \: (2\pi \: - (\pi)/(4) ) \: \: ( (3\pi)/(2) < theta < 2\pi)`

`= cos \: (7\pi)/(4)`

Theta = 7π / 4

`sin \: theta = sin \: (7\pi)/(4)`

`= sin \: (2\pi \: - (\pi)/(4) )`

`- sin \: (\pi)/(4)`

`= ( - 1)/( √(2) )`

`= - ( √(2) )/(2)`

Finding tan theta:

`tan \: theta = tan \: (7\pi)/(4)`

`=tan \: (2\pi - (\pi)/(4) )`

`= - tan \: (\pi)/(4)`

`= - 1`

Hope this helps...

Good luck on your assignment...

Answer 2

tan =-1

Explanation:

tan(θ)=sen(θ)/cos(θ)

so

`tan(angle)=((-√(2) )/(2) )/((√(2) )/(2) ) }\\\\tan(angle)=-1`