STEP - BY - STEP EXPLANATION
What to find?
The the value of secθ.
Given:
(4, 3)
⇒(x, y) = (4, 3)
Step 1
Draw a sketch.
Step 2
Substitute the values into the trig. ratio formula below.
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
From the sketch above, opposite = 3 and adjacent = 4
[tex]tan\theta=\frac{3}{4}[/tex]
Step 3
Find the value of the hypotenuse side using Pythagoras theorem.
let h be the hypotenuse side.
[tex]\begin{gathered} h^2=4^2+3^2 \\ \\ =16+9 \\ \\ =25 \\ \\ h=5 \end{gathered}[/tex]
Hence, hypotenuse = 5
Step 4
Substitute the values into the formula below:
[tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ \\ =\frac{4}{5} \end{gathered}[/tex]
But,
[tex]sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{4}{5}}=\frac{5}{4}[/tex]
ANSWER
secθ= 5/4
tanθ=3/4
