How do you find the exact value of sec(arcsin(4/5))?
2 Answers
Explanation:
Let
Therefore:
sin^2(theta) = 16/25
1 - sin^2(theta) = 1 - 16/25
1 - sin^2(theta) = 9/25
cos^2(theta) = 9/25
cos(theta) = +-3/5
Note that
cos(theta) = 3/5
sec(theta) = 5/3
sec(arcsin(4/5)) = 5/3
Final Answer
Explanation:
Alternatively, use the 3-4-5 right triangle as a shortcut to the problem.
We can see that
Therefore, we can say that
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We can also see that
Therefore,
sec(theta) = 1/cos(theta) = 5/3
And, since we know
sec(arcsin(4/5)) = 5/3
Final Answer