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.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.