Question

Find the values of trigonometric ratios and the value of θ​

Answer 1

Answer:

Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Cosecant is the reciprocal of sine, so the cosecant of any angle x for which sin x = 0 must be undefined, since it would have a denominator equal to 0. The value of sin (0) is 0, so the cosecant of 0 must be undefined.

Answer 2

Given:

A right-angled triangle ABC with 90° angle at B.

To Find: Trigonometric ratios and value of θ

Calculation:

From the figure below,

sin θ = $\frac{perpendicular}{hypotenuse}$ = $\frac{AB}{AC}$ $=\frac{p}{h}$

cos θ = $\frac{base}{hypotenuse} =\frac{BC}{AC}$ $=\frac{b}{h}$

tan θ = $\frac{perpendicular}{base} =\frac{AB}{BC} =\frac{p}{b}$

θ = $tan^{-1} \frac{p}{b}$

Answer:

Value of angle θ = $tan^{-1} (\frac{p}{b})$