Processing math: 100%

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Trigonometrical Ratios of 0°

How to find the Trigonometrical Ratios of 0°?

Let a rotating line OX rotates about O in the anti clockwise sense and starting from its initial position OX traces out ∠XOY = θ where θ is very small.

Trigonometrical Ratios of 0°

Take a point P on OY  and draw ¯PQ perpendicular to OX  .

Now according to the definition of trigonometric ratio we get,
sin θ = ¯PQ¯OP;
cos θ = ¯OQ¯OP and
tan θ = ¯PQ¯OQ           

When θ is slowly decreases and finally tends to zero then,
(a) ¯PQ slowly decreases and finally tends to zero and

(b) the numerical difference between ¯OP  and ¯OQ  becomes very small and finally tends to zero.

Hence, in the Limit when θ → 00 then ¯PQ → 0 and ¯OP   → ¯OQ  . Therefore, we get
limθ0sinθ=limθ0¯PQ¯OP=0¯OQ [since, θ → 0° therefore, ¯PQ → 0].
= 0

Therefore sin 0° = 0

limθ0cosθ=limθ0¯OQ¯OP=¯OQ¯OQ, [since, θ → 0° therefore, ¯OP¯OQ].
= 1

Therefore cos 0° = 1

limθ0tanθ=limθ0¯PQ¯OQ=0¯OQ [since, θ → 0° therefore, ¯PQ → 0].
= 0

Therefore tan 0° = 0

Thus,
csc 0° = 1sin0°=10, [since, sin 0° = 0] 
= undefined

Therefore csc 0° = undefined


sec 0° = 1cos0°=11, [since, cos 0° = 1] 
= 1

Therefore sec 0° = 1


cot 0° = 1tan0°=10, [since, tan 0° = 0] 
= undefined

Therefore cot 0° = undefined

Trigonometrical Ratios of 0 degree are commonly called standard angles and the trigonometrical ratios of these angles are frequently used to solve particular angles.

 Trigonometric Functions







11 and 12 Grade Math

From Trigonometrical Ratios of 0° to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.