# How do you find the exact value of #arccos(sin(3*pi/2))#?

##### 2 Answers

#### Explanation:

You need to covert the expression involving the

There are always several ways to manipulate trig functions, however one of the most straight forward ways to covert an expression involving sine into one for cosine is to use the fact that they are the SAME FUNCTION just shifted over by

So we replace

or

There is the odd issue with multiple solutions to many expressions involving inverse trig functions. The most obvious relates to

Because of the periodicity of the cosine function with have

The real issue here is the inverse cosine, cosine is a function with has multiple y values so when you reverse it you actually get an infinite number of possible answers, when we use it we RESTRICT the values to a window of

#### Explanation:

We have,

Hence, reqd. value

Then, by defn. of