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asked Jan 26, 2020 139k views

2 Answers

Jcardenete · Answer 1 · 2020-01-31T02:49:59+0000

QUESTION 18

Use the Pythagorean Identity.

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

We substitute the given value into the formula,

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

$\cos^(2)( \theta) + (16)/(49) = 1$

$\cos^(2)( \theta) = 1 - (16)/(49)$

$\cos^(2)( \theta) = (33)/(49)$

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

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

$\cos( \theta) = ( √(33))/(7)$

The 3rd choice is correct.

QUESTION 19.

We want to simplify;

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

Recall the reciprocal identity

$\sec( \theta) = (1)/( \cos( \theta) )$

This implies that,

$18 \sin( \theta) \sec( \theta) =18 \sin( \theta) * (1)/( \cos( \theta) )$

$18 \sin( \theta) \sec( \theta) =18 * (\sin( \theta) )/( \cos( \theta) )$

This will give us:

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

The correct choice is D.