Question

Given sin θ = 3/5 what is sec θ?

Answer 1

Answer:

5/4

Step-by-step explanation:

To do this you must know that by definition secant is:

$sec(\theta)=\frac{1}{cos(\theta)}$

Furthermore:

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}$

Based on this information we know that 3 = opposite and 5 = hypotenuse.  Assuming this is a right triangle we can determine the adjacent side by Pythagorean Theorem.

$c^2=a^2+b^2$

Where c is the hypotenuse, a is adjacent and b is opposite.  Therefore,

$c^2=a^2+b^2\\\\a=\sqrt{c^2-b^2} \\\\a=\sqrt{5^2-3^2} \\\\a=4$

And so the adjacent side of this triangle is 4.  Going back to the definition of secant we can now know that:

$sec(\theta)=\frac{1}{cos(\theta)}=\frac{1}{\frac{4}{5}}=\frac{5}{4}$

Answer 2

The correct answer is D 5/4 :)