Question

Given the right triangle find the value of sec(90 degree - theta) when a= 12, b= 5, c= 13

Answer 1

Use the next trigonometric identities:

`\begin{gathered} \sec (90º-\theta)=(1)/(\cos (90º-\theta)) \\ \\ \cos (90º-\theta)=\sin \theta \end{gathered}`

Then, the sec(90º - θ) is:

`\sec (90º-\theta)=(1)/(\sin \theta)`

The sin(θ) is:

`\sin \theta=(opposite)/(hypotenuse)=(5)/(13)`

Then:

`\sec (90º-\theta)=(1)/((5)/(13))=(13)/(5)`

Then, the sec(90º - θ) is 13/5