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=(opposite)/(adjacent)`

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

`tan\theta=(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=(adjacent)/(hypotenuse) \\ \\ =(4)/(5) \end{gathered}`

But,

`sec\theta=(1)/(cos\theta)=(1)/((4)/(5))=(5)/(4)`

ANSWER

secθ= 5/4

tanθ=3/4