Question

evaluate sec(sin^-1 4/5)

Answer 1

Suppose \(\theta=\sin^{-1}\dfrac{4}{5}\), so that \(\sin\theta=\dfrac{4}{5}\). This gives you a triangle:

What's the length of the missing side?

If \(\theta\) is the angle on the left, what would its secant be?

Answer 2

sin of -4/5

Answer 3

Um, what?

Answer 4

Guessing I am not really that good with this trig stuff

Answer 5

From the Pythagorean theorem, you get
\[\begin{align*}x^2+4^2&=5^2\\
x^2&=25-16\\
x^2&=9\\
x&=3
\end{align*}\]
So if \(\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}}\) and \(\sec\theta=\dfrac{1}{\cos\theta}\), what do you get?

Answer 6

5/3

Answer 7

Correct