Question

Given sin(0) = -1/4 and tan 0 = squareroot of 15/15. what is the value of cos 0?

Answer 1

`\cos \theta = (√(15))/(4)}`

Explanation:

Recall that
`\sin(-\theta)=-\sin(\theta)`. Therefore,
`\sin\theta=-(-(1)/(4))=(1)/(4)`

In any right triangle:

• The sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle (o/h)

• The cosine of an angle is equal to its adjacent side divided by the hypotenuse of the triangle (a/h)

• The tangent of an angle is equal to its opposite side divided by its adjacent side (o/a)

From
`\sin \theta=(1)/(4)` and
`\tan \theta = (√(15))/(15)`, we know:

• 
  `\theta`'s opposite side is 1
• 
  `\theta`'s adjacent side is
  `√(15)`
• The hypotenuse of the triangle is 4

Therefore, the desired answer is
`\boxed{\cos \theta = (√(15))/(4)}}`.