To find the value of an expression where multiple trigonometric functions are involved, use a calculator.
0.6
Practice makes perfect
We want to find the value of an expression that has multiple trigonometric functions.
cos ( Arcsin 4/5)
To do so we will use a calculator. We push COS and then 2ND, followed by SIN. Finally, we introduce the value 45 and push ENTER. This will give us the value of cos ( Arcsin 45). Recall that Arcsin is the same as sin^(- 1).
We found that the value of cos ( Arcsin 45) is 0.6.
Checking Our Answer
We can check our answer by doing each of the calculations separately — calculating the inverse sine of 45 and then the cosine of this result. To do so, we push 2ND in our calculator followed by SIN, introduce the value 45, and push ENTER.
The inverse sine of 45 is about 53.13^(∘). Now we will calculate the cosine of 53.13^(∘). To do so, we push COS, put in the value 53.13, and push ENTER.
The cosine of 53.13^(∘) 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.
