Question

Find secθ, sinθ, and tanθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.secθ=sinθ=tanθ=

Answer 1

The given triangle is a right angle triangle.

We would determine the unknown side by applying pythagoras theorem which is expressed as

hypotenuse^2 = opposite side^2 + adjacent side^2

Looking at the triangle, with θ as the reference angle,

hypotenuse = 12

opposite side = 12

adjacent side = unknown side

thus,

adjacent side^2 = 13^2 - 12^2 = 169 - 144 = 25

$\begin{gathered} \text{adjacent side = }\sqrt[]{25} \\ \text{adjacent side = 5} \end{gathered}$

secθ = 1/cosecθ

To find secθ, we would first find cosecθ

To determine cosecθ, we would apply the cosine trigonometeric ratio.

Cosθ = adjacent side/hypotenuse

Cosθ = 5/13

Since Secθ = 1/cosθ, it means that

secθ = 1/(5/13) = 1 * 13/5

Secθ = 13/5 = 2.6

Sinθ = opposite side/hypotenuse = 12/13

Sinθ = 12/13

Tanθ = opposite side/adjacent side = 12/5

Tanθ = 2.4