QUESTION 18
Use the Pythagorean Identity.
[tex] \cos^{2}( \theta) +\sin^{2}( \theta) = 1[/tex]
We substitute the given value into the formula,
[tex] \cos^{2}( \theta) +( { \frac{4}{7} })^{2} = 1[/tex]
[tex] \cos^{2}( \theta) + \frac{16}{49} = 1[/tex]
[tex] \cos^{2}( \theta) = 1 - \frac{16}{49} [/tex]
[tex]\cos^{2}( \theta) = \frac{33}{49} [/tex]
Since we are in the first quadrant, we take positive square root,
[tex]\cos( \theta) = \sqrt{\frac{33}{49} } [/tex]
[tex]\cos( \theta) = \frac{ \sqrt{33}}{7} [/tex]
The 3rd choice is correct.
QUESTION 19.
We want to simplify;
[tex]18 \sin( \theta) \sec( \theta) [/tex]
Recall the reciprocal identity
[tex] \sec( \theta) = \frac{1}{ \cos( \theta) } [/tex]
This implies that,
[tex]18 \sin( \theta) \sec( \theta) =18 \sin( \theta) \times \frac{1}{ \cos( \theta) } [/tex]
[tex]18 \sin( \theta) \sec( \theta) =18 \times \frac{\sin( \theta) }{ \cos( \theta) } [/tex]
This will give us:
[tex]18 \sin( \theta) \sec( \theta) =18 \tan( \theta) [/tex]
The correct choice is D.
