1. This is straightforward - use the `sin^-1` button on your calculator:

θ = sin-1 0.6235 = 38.572°

This is equivalent to (and better):

θ = arcsin 0.6235 = 38.572°


2. This one uses the `tan^-1` button:

θ = tan-1 3.689 = 74.833°

This is equivalent to:

θ = arctan 3.689 = 74.833°

Can you draw a triangle to illustrate what this means? Go on, try - it really helps to understand it.


3. We have to do some thinking for this one. There is no `csc^-1` button on our calculators, so we need to proceed as follows.

csc θ = 8.32,

so

`sin\ θ = 1/8.32 = 0.12019`. (since `sin\ θ` is the reciprocal of `csc\ θ`).

Now we can use the `sin^-1` button to obtain:

θ = sin-1 0.12019 = arcsin 0.12019 = 6.9032°


4. Similar to Q3, we need to find the reciprocal first.

`sec\ θ = 6.96`, giving us `cos\ θ = 1/6.96 = 0.143678`.

Therefore

θ = cos-1 0.143678 = arccos 0.143678 = 81.739°