Question

Please help me thank you

Answer 1

solution for #18 is C and for #19 is D

Answer 2

QUESTION 18

Use the Pythagorean Identity.

$\cos^{2}( \theta) +\sin^{2}( \theta) = 1$

We substitute the given value into the formula,

$\cos^{2}( \theta) +( { \frac{4}{7} })^{2} = 1$

$\cos^{2}( \theta) + \frac{16}{49} = 1$

$\cos^{2}( \theta) = 1 - \frac{16}{49}$

$\cos^{2}( \theta) = \frac{33}{49}$

Since we are in the first quadrant, we take positive square root,

$\cos( \theta) = \sqrt{\frac{33}{49} }$

$\cos( \theta) = \frac{ \sqrt{33}}{7}$

The 3rd choice is correct.

QUESTION 19.

We want to simplify;

$18 \sin( \theta) \sec( \theta)$

Recall the reciprocal identity

$\sec( \theta) = \frac{1}{ \cos( \theta) }$

This implies that,

$18 \sin( \theta) \sec( \theta) =18 \sin( \theta) \times \frac{1}{ \cos( \theta) }$

$18 \sin( \theta) \sec( \theta) =18 \times \frac{\sin( \theta) }{ \cos( \theta) }$

This will give us:

$18 \sin( \theta) \sec( \theta) =18 \tan( \theta)$

The correct choice is D.