We want to find the value of an expression that has multiple trigonometric functions.

cos (A r c s i n \frac{4}{5})

To do so we will use a calculator. We push

COS

and then

2 ND,

followed by

SIN .

Finally, we introduce the value

\frac{4}{5}

and push

ENTER .

This will give us the value of

cos (A r c s i n \frac{4}{5}) .

Recall that Arcsin is the same as

sin^{- 1} .

We found that the value of

cos (A r c s i n \frac{4}{5})

is

0.6 .

Checking Our Answer

We can check our answer by doing each of the calculations separately — calculating the inverse sine of $\frac{4}{5}$ and then the cosine of this result. To do so, we push $2 ND$ in our calculator followed by $SIN,$ introduce the value $\frac{4}{5},$ and push $ENTER .$

The inverse sine of $\frac{4}{5}$ is about $53.1 3^{\circ} .$ Now we will calculate the cosine of $53.1 3^{\circ} .$ To do so, we push $COS,$ put in the value $53.13,$ and push $ENTER .$

The cosine of $53.1 3^{\circ}$ is about $0.6 .$ Since the last value we used is rounded, the result is slightly different than our answer. However, we can still conclude that the answer in our solution is correct.

Exercise