Question

Those 2 questions I need help with . find sec θ and tanθ

Answer 1

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.

$tan\theta=\frac{opposite}{adjacent}$

From the sketch above, opposite = 3 and adjacent = 4

$tan\theta=\frac{3}{4}$

Step 3

Find the value of the hypotenuse side using Pythagoras theorem.

let h be the hypotenuse side.

$\begin{gathered} h^2=4^2+3^2 \\ \\ =16+9 \\ \\ =25 \\ \\ h=5 \end{gathered}$

Hence, hypotenuse = 5

Step 4

Substitute the values into the formula below:

$\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ \\ =\frac{4}{5} \end{gathered}$

But,

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

ANSWER

secθ= 5/4

tanθ=3/4