Question

Question #aa712

Answer 1

`theta=147.4°`

Explanation:

First, recall the following identity:

`sin(x+90°)=cos(x)`

Graphically interpreted, this identity tells us that if we shift the sine curve to the left by `90°`, we get the cosine function. This identity goes both ways, meaning that `cos(x)=sin(x+90°)`.

Therefore, we can rewrite `cos(57.4°)` as `sin(57.4°+90°)`:

`sin(theta)=sin(57.4°+90°)`

`57.4°+90°=147.4°`

`sin(theta)=sin(147.4°)`

`theta=147.4°`

Answer 2

It is given that, `sin(θ)=cos(57.4∘)`

We know that, `color(red)(sintheta = cos(90-theta)`

therefore,
`cos57.4 = cos(90-32.6)`
`cos57.4 = sin 32.6`

Hence, `theta = 32.6`