1 Answer

Bruce Barnett · Answer 1 · 2023-07-20T11:25:45+0000

Given that cot(0) = 4/3 and theta is in Quadrant I, what is sin(theta)?

we have that

If angle theta is in quadrant I , then the value of sin(theta) is positive

Remember that

$\tan ^2\theta+1=\sec ^2\theta$

tan(theta)=1/cot(theta)

so

tan(theta)=3/4

substitute in the expression above

$((3)/(4))^2+1=\sec ^2\theta$
$\sec ^2\theta=(25)/(16)$
$\sec ^{}\theta=(5)/(4)$

is positive because is quadrant I

remember that

sec(theta)=1/cos(theta)

so

cos(theta)=4/5

tan(theta)=3/4

tan(theta)=sin(theta)/cos(theta)

substitute given values

3/4=sin(theta)/(4/5)

sin(theta)=(3/4)*(4/5)=3/5

the answer is

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