Question

5. Cos 0 = -4/21 and 0 lies in quadrant 3

Answer 1

Given:

$\cos\emptyset=\frac{-4}{21}$

Required:

Find all other trigonometric ratio

Explanation:

Here angle is in third quadrant so only tan and cot are positive

here we have one side and hypotenuse

with the help of these two we can find another side by Pythagorean theorem

$x=\sqrt{21^2-4^2}=\sqrt[]{425}$

now we have all the sides

now we can find all the remaining ratio

Final answer:

$\sin\emptyset=\frac{-\sqrt[]{425}}{21}$$\tan\emptyset=\frac{\sin\emptyset}{\cos\emptyset}=\frac{4}{\sqrt{425}}$$cot\emptyset=\frac{1}{\tan\emptyset}=\frac{\sqrt[]{425}}{4}$$sec\emptyset=\frac{1}{cos\emptyset}=\frac{-21}{4}$$cosec\emptyset=\frac{1}{sin\emptyset}=\frac{-21}{\sqrt[]{425}}$