Sec 0

The ratio of the length of the hypotenuse to the length of the adjacent side is the secant of an angle in a right-angled triangle. Consider a triangle RST the secant 0 value of the triangle is the Hypotenuse / Adjacent side. 

Cosecant can be used in place of Secant in the form: Secant = \[\frac{1}{Cosecant}\].

The Inverse Secant x Formula

An inverse function that works in reverse exists for every trigonometric function. All these trigonometric functions start with “arc” in their names. Even the secant has a reverse name and it goes by arcsec. 

How to Calculate Sec 0 Degree?

We know that the first quadrant is between 0 degrees and 90 degrees. In this quadrant, the values of sine, cosine, and tangent are positive. Besides that, we also know that the right angle is always equal to 90 degrees. 

sec y = \[\frac{1}{cosec (y)}\]

sec 0 = \[\frac{1}{cosec (0)}\]

sec 0 = \[\frac{1}{1}\]

sec 0 = 1

Important Formulas in Trigonometry

1.  sin-1 ( - y ) = - sin -1 ( y ), y Є [ - 1, 1 ]

2. cos-1 ( - y ) = pi* - cos -1 ( y ), y Є [ - 1, 1 ]

3.  tan-1 ( - y ) = - tan -1 ( y ), y Є R

4. cosec-1 ( - y ) = - cosec -1 ( y ), | y | ≥ 1

5. sec -1 ( - y ) = pi - sec -1 ( y ), | y | ≥ 1

6. cot -1 ( - y ) = pi - cot -1 ( y ),  y Є R

7. sin-1 ( - y ) + cos-1 ( - y ) = pi /2 ,  y Є [ - 1, 1 ]

8. tan-1 ( - y ) + cot -1 ( - y ) =  pi /2 ,  y Є R

9. sec -1 ( - y ) + cosec-1 ( - y ) = pi /2 ,  | y | ≥ 1

10.  Sin -1 ( 1 / y ) = cosec -1 ( y ), if y ≥ 1 or y ≤ - 1

11.  cos -1 ( 1 / y ) = sec -1 ( y ), if y ≥ 1 or y ≤ - 1

12.  tan -1 ( 1 / y ) = cot -1 ( y ), if y > 0

13.  tan-1 x + tan-1 y = tan-1 ((x + y) / (1 - xy)), if the value xy < 1

14.  tan-1 x - tan-1 y = tan-1 ((x - y) / (1 + xy)), if the value xy > - 1

15.  2 tan  -1 y = sin -1 ( 2x / ( 1 + x2 )), | x | ≤  1

16.  2 tan  -1 y = cos-1 (( 1- y2)/(1+ y2)), y ≥ 0

17.  2 tan-1  = tan-1 ( 2y / (1-y2 )), -1 < y < 1

18.  3sin-1 y = sin-1 ( 3x - 4y3)

19.  3cos-1 y = cos-1 ( 4y3 -3y )

20.  3tan-1 y = tan-1 (( 3y - y3 ) / (1 - 3y2))

21.  sin(sin-1 ( y )) = y, -1 ≤  y  ≤ 1

22. cos ( cos-1 ( y ) ) = y, -1≤ y ≤1

23. tan (tan-1 ( y )) = y , – ∞ < x < ∞

24. cosec ( cosec-1 ( y )) = y, – ∞ < y ≤ 1 or -1 ≤ y < ∞

25. sec (sec-1 ( y )) = y,- ∞ < y ≤ 1 or 1 ≤ y < ∞

Sample Questions

Question 1: Find the value of tan y if secant y is equal to 1.

Solution: 

sec 2 y = 1 + tan 2 y

sec 2 y - 1 = tan 2 y

( 1 )2 - 1 = tan 2 y

1 - 1 = tan 2 y

tan 2 y = 0

tan y = \[\sqrt 0\]

tan y = 0