Question

if tan theta =-3/4then find the value of sintheta ,costheta and cot theta

Answer 1

Given that,

tan∅ = -3/4

We know that tan∅ = P/B

where P = perpendicular and B = base.

So let P be -3x and B be 4x

Now, we can find the hypotenuse,

so, hypotenuse =
$\sqrt{(-3x) {}^{2} + (4x) {}^{2} } \\ \\ = > \sqrt{9 {x}^{2} + 16 {x}^{2} } \\ \\ = > \sqrt{25 {x}^{2} } \\ \\ = > 5x$

So hypotenuse = ±5x

We know that, sin∅ = P/H

P = -3x
H = 5x

=> sin∅ = -3x/5x

=> sin∅ = -3/5

Similarly, cos∅ = B/H

B = 4x
H = 5x

=> cos∅ = 4x/5x

=> cos∅ = 4/5

Now cot∅ is reciprocal of tan∅

Given tan∅ = -3/4

=> cot∅ = 4/-3

=> cot∅ = -4/3

Your answers :-
sin∅ = -3/5
cos∅ = 4/5
cot∅ = -4/3

Hope it helps dear friend ☺️

Answer 2

tan theta =-3/4

sin theta=-3/5

cos theta=4/5

cot theta=-4/3