Question

For an acute angle θ, the equation sin(θ)=cos(6) is true. What is the value of θ? Show or explain your answer

Answer 1

The value of θ in the equation sin(θ) = cos(6) is 84 degrees.

Step-by-step explanation:

For an acute angle θ, the equation sin(θ)=cos(6) is true. To find the value of θ, we can use the fact that sin(θ) = cos(90 - θ). So, we have sin(θ) = sin(90 - 6). Since sin(θ) and sin(90 - 6) are equal, we can set the angles equal to each other and solve for θ. 90 - 6 = θ, so θ = 84 degrees.

Answer 2

`\theta= 84`

Step-by-step explanation:

Given

`\sin(\theta) = \cos(6)`

Required

Find
`\theta`

In trigonometry,

If
`\sin(\theta) = \cos(\alpha)`, then

`\theta + \alpha = 90`

So, in this case:

`\theta + 6= 90`

Subtract 6 from both sides

`\theta + 6-6= 90-6`

`\theta= 90-6`

`\theta= 84`

Hence, the value of
`\theta` is 84 degrees