Question

If cot theta = 4/3, then find the value of sin theta, cos theta and cosec theta in first quadrant.

Answer 1

$\cot(theta) = \frac{4}{3} = \frac{base}{perpendicular} \\ {sin(theta)} = \frac{perpendicular}{hypotenuse} \\ \cos(theta) = \frac{base}{hypotenuse} \\ \: hypotenuse = \sqrt{ {4}^{2} + {3}^{2} } = \sqrt{16 + 9} \\ = \sqrt{25} = 5 \\ \sin(theta) = \frac{3}{5} \\ \cos(theta) = \frac{4}{5} \\ cosec(theta) = \frac{1}{ \sin(theta) } \\ = \frac{5}{3} \\ all \: being \: positive \: because \: of \: in \: first \: quadrant$

Answer 2

Step-by-step explanation:

ot(theta)=

3

4

=

perpendicular

base

sin(theta)=

hypotenuse

perpendicular

cos(theta)=

hypotenuse

base

hypotenuse=

4

2

+3

2

=

16+9

=

25

=5

sin(theta)=

5

3

cos(theta)=

5

4

cosec(theta)=

sin(theta)

1

=

3

5

allbeingpositivebecauseofinfirstquadrant