Question #3d0cd

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Answer 1 · 2017-04-06T15:39:45

$cos theta = - 3/( sqrt 10)$

$sin theta = +1 /sqrt 10$

$tan theta = -1/3$

$cos 2theta = 4/5$

a. $cos^2 theta - sin^2 theta = 4/5$

$cos^2 theta - (1 -cos^2 theta) = 4/5$

$2cos^2 theta - 1 = 4/5$

$2cos^2 theta = 4/5 + 1 = 9/5$

$cos^2 theta = 9/10$

$cos theta = -sqrt (9/10) = - 3/( sqrt 10)$ -> quadrant II

b. $cos^2 theta - sin^2 theta = 4/5$

$(1- sin^2 theta) - sin^2 theta = 4/5$

$(1 - 2sin^2 theta) = 4/5$

$(1 - 4/5) = 2sin^2 theta$

$2sin^2 theta = 1/5$

$sin^2 theta = 1/10$

$sin theta = +sqrt(1/10) = +1 /sqrt 10$ -> quadrant II

c. $tan theta = sin theta/cos theta = +1 /sqrt 10/- 3/( sqrt 10)$

$tan theta = -1/3$ -> quadrant II