If cos theta=-2/3, which of the following are possible (Help asap)

Question

asked May 20, 2019 97.2k views

2 Answers

Dave Schweisguth · Answer 1 · 2019-05-26T23:35:05+0000

Answer:

The correct option is B)
$sin\theta=(√(5))/(3)$ and
$tan\theta=(√(5))/(2)$

Explanation:

given
$cos\theta=-(2)/(3)$

Since,
$cos\theta=(base)/(hypoteneous)$

it means prependicular of right angled triangle can be calculated by pythagoras theorem as:

base² + prependicular² = hypoteneous²

2² + prependicular² = 3²

4 + prependicular² = 9

prependicular² = 9 - 4

prependicular² = 5

prependicular = √5

Since,
$sin\theta=(prependicular)/(hypoteneous)$

$sin\theta=(√(5))/(3)$

Since,
$tan\theta=(prependicular)/(base)$

$tan\theta=(√(5))/(2)$

Hence, the correct option is B)
$sin\theta=(√(5))/(3)$ and
$tan\theta=(√(5))/(2)$