Question

Given that cosine theta = -1/2, and theta is obtuse, find:

a) sine theta

b) sine 2(theta)

c) tangent theta

d) sine 4(theta)

Answer 1

Answers:

a) 0.86

b) -0.86

c) -1.73

d) 0.86

Explanation:

We are told
`cos \theta=-(1)/(2)`. So, we first have to find the value of
`\theta` which is an obtuse angle (an angle greater than
`90\°` and smaller than
`180\°`):

`\theta=cos^(-1) (-(1)/(2))`

`\theta=120\°`

Now that we know the value of the angle
`\theta`, let's begin with the answers:

a)
`sin \theta=sin (120\°)=0.86`

b)
`sin 2\theta=sin (2(120\°)=sin (240\°)=-0.86`

c)
`tan \theta=tan (120\°)=-1.73`

d)
`tan 4\theta=sin (4(120\°)=sin (480\°)=0.86`