Question

What is the correct definition for tan 0

tan0=1/sin0
tan0=1/cos0
tan0=cos0/sin0
tan0=sin0/cos0
please explain if possible.

Answer 1

The correct definition for the tangent of an angle is the ratio of the sine of that angle to the cosine of the same angle, expressed as tan(theta) = sin(theta) / cos(theta).

Step-by-step explanation:

The correct definition for tan(θ) is tan(θ) = sin(θ) / cos(θ). In trigonometry, the tangent of an angle in a right-angled triangle is defined as the ratio of the opposite side to the adjacent side. The tangent function is one of the three primary trigonometric functions, along with sine and cosine. Because the definition directly relates to the sides of a right triangle, it's applicable to various geometry and trigonometry problems.

Answer 2

`tan\theta=(sin\theta)/(cos\theta)\\\\\\Look\ at\ the\ picture.\\\\In\ a\ right\ triangle:\\\\sin\theta=(a)/(c);\ cos\theta=(b)/(c);\ tan\theta=(a)/(b)\\\\(sin\theta)/(cos\theta)=((a)/(c))/((b)/(c))=(a)/(c)*(c)/(b)=(a)/(b)=tan\theta`