Sec, cosec and cot are trigonometry ratios. The ratio between the hypotenuse and opposite is called as cosec. The ratio between hypotenuse and adjacent side is called as sec. The ratio between adjacent and opposite side is called as cot. Let us see sec, cosec and cot in this article.

**Trigonometry ration:**

Consider the above triangle. Based on the position of `theta` we can identify the opposite side and adjacent side.

**Cosec:**

- The ratio between the length of hypotenuse and length of opposite side is known as cosec.
- Cosec is reciprocal of sin (cosec`theta` = `(hypo)/(opposite)` ).
- Cosec `theta` = `(1)/(sintheta)`
- Cosec is also written as csc and cosecant.

**Sec:**

- The ratio between the length of hypotenuse and length of adjacent side is known as sec.
- Sec is reciprocal of sin (sec `theta` = `(hypo)/(adjacent)`).
- Sec `theta` = `(1)/(costheta)`
- Sec is also written as secant.

**Cosec:**

- The ratio between the length of adjacent side and length of opposite is known as cot.
- Cot is reciprocal of tan(cot `theta`= `(adjacent)/(opposite)`).
- Cot `theta` = `(1)/(tantheta)`
- Cot is also written as cotangent.

**Problem 1:**

In right angled triangle the opposite and hypotenuse side is 4 and 7 respectively. Measure the cosec value.

**Solution:**

Given

The opposite side value of right angled triangle = 4

The hypotenuse side value of right angled triangle = 7

Cosec `theta` = `(hypo)/(opposite)`

Apply the given in above formula

Cosec `theta` = `(7)/(4)`

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**Problem 2:**

If Cos X = 4/7 then calculate the sec X value.

**Solution:**

Given

Cos X = 4/7

Sec X =?

We know that

Cos X = `(adjacent)/(hypoten)`

Compare the given with above structure, now we get

Adjacent side = 4

Hypotenuse = 7

Sec `theta` = `(hypo)/(adjacent)`

Substitute the adjacent and hypotenuse value

Sec `theta` = `(7)/(4)`

**Problem 3:**

If sin X = 3/5 and cos X = 4/5 then find cot X value.

**Solution:**

Given

Sin X = 3/5

Cos X = 4/5

Cot X =?

We know that

Sin `theta` = `(opposite)/(hypo)`

Compare Sin X = 3/5 with Sin `theta` = `(opposite)/(hypo)`

From above comparison we know that

Opposite side value = 3

Hypotenuse value = 5

We know that

Cos `theta` = `(adjacent)/(hypo)`

Compare cos X = 4/5 with Cos `theta` = `(adjacent)/(hypo)`

From above comparison we know that

Adjacent side value = 4

**Hypotenuse** value = 5

Cot `theta`= `(adjacent)/(opposite)`

Substitute the opposite side and adjacent side value

Cot `theta` = `(4)/(3)`