Evaluate each of the following expressions without using a calculator. use radian measures.
e. sin−1(1) f. sin−1(−1)
g. cos−1(1) h. cos−1(−1)
i. tan−1(1) j. tan−1(−1)

e)

f)

g)

h)

i)

j)

Step-by-step explanation:

We can solve this exercise by watching a basic trigonometric table

Here i will list values of sin and cos in the points  and

Hence, the sin takes the value 1 on , while it takes the value -1 in its opposite value - \pi/2 (because it is an odd function). If we use the periodicity of the sin, then sin(- \pi/2 + 2 \pi) = -1. Hence

The cos takes value 1 in 0, and it takes the value -1 in

The tangent is the quotient between sin and cos. The tangent is 1 when both cos and sin are equal. We can see that they are equal in , where they take the value

The tangent is -1 where they are the opposite. This happens in where they take the value and respectively.

answer:

this statement is true.