sec 0 Value
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
sin-1 ( - y ) = - sin -1 ( y ), y Є [ - 1, 1 ]
cos-1 ( - y ) = pi* - cos -1 ( y ), y Є [ - 1, 1 ]
tan-1 ( - y ) = - tan -1 ( y ), y Є R
cosec-1 ( - y ) = - cosec -1 ( y ), | y | ≥ 1
sec -1 ( - y ) = pi - sec -1 ( y ), | y | ≥ 1
cot -1 ( - y ) = pi - cot -1 ( y ), y Є R
sin-1 ( - y ) + cos-1 ( - y ) = pi /2 , y Є [ - 1, 1 ]
tan-1 ( - y ) + cot -1 ( - y ) = pi /2 , y Є R
sec -1 ( - y ) + cosec-1 ( - y ) = pi /2 , | y | ≥ 1
Sin -1 ( 1 / y ) = cosec -1 ( y ), if y ≥ 1 or y ≤ - 1
cos -1 ( 1 / y ) = sec -1 ( y ), if y ≥ 1 or y ≤ - 1
tan -1 ( 1 / y ) = cot -1 ( y ), if y > 0
tan-1 x + tan-1 y = tan-1 ((x + y) / (1 - xy)), if the value xy < 1
tan-1 x - tan-1 y = tan-1 ((x - y) / (1 + xy)), if the value xy > - 1
2 tan -1 y = sin -1 ( 2x / ( 1 + x2 )), | x | ≤ 1
2 tan -1 y = cos-1 (( 1- y2)/(1+ y2)), y ≥ 0
2 tan-1 = tan-1 ( 2y / (1-y2 )), -1 < y < 1
3sin-1 y = sin-1 ( 3x - 4y3)
3cos-1 y = cos-1 ( 4y3 -3y )
3tan-1 y = tan-1 (( 3y - y3 ) / (1 - 3y2))
sin(sin-1 ( y )) = y, -1 ≤ y ≤ 1
cos ( cos-1 ( y ) ) = y, -1≤ y ≤1
tan (tan-1 ( y )) = y , – ∞ < x < ∞
cosec ( cosec-1 ( y )) = y, – ∞ < y ≤ 1 or -1 ≤ y < ∞
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
FAQs on Sec 0
1) What is 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. Cosecant can be used in place of Secant in the form: Secant = 1 / Cosecant. Now, let’s calculate the sec 0 value.
sec y =1/cosecant y
sec 0 = 1/cosecant 0
sec 0 = 1/1
sec 0 = 1
2) What are the Important Trigonometric Formulas?
sin-1 ( - y ) = - sin -1 ( y ), y Є [ - 1, 1 ]
cos-1 ( - y ) = pi* - cos -1 ( y ), y Є [ - 1, 1 ]
tan-1 ( - y ) = - tan -1 ( y ), y Є R
cosec-1 ( - y ) = - cosec -1 ( y ), | y | ≥ 1
sec -1 ( - y ) = pi - sec -1( y ), | y | ≥ 1
cot -1 ( - y ) = pi - cot -1 ( y ), y Є R
sin-1 ( - y ) + cos-1 ( - y ) = pi /2 , y Є [ - 1, 1 ]
tan-1 ( - y ) + cot -1 ( - y ) = pi /2 , y Є R
sec -1 ( - y ) + cosec-1 ( - y ) = pi /2 , | y | ≥ 1
Sin -1 ( 1 / y ) = cosec -1 ( y ), if y ≥ 1 or y ≤ - 1
cos -1 ( 1 / y ) = sec -1 ( y ), if y ≥ 1 or y ≤ - 1
tan -1 ( 1 / y ) = cot -1 ( y ), if y > 0
tan-1 x + tan-1 y = tan-1 ((x + y) / (1 - xy)), if the value xy < 1
tan-1 x - tan-1 y = tan-1 ((x - y) / (1 + xy)), if the value xy > - 1
2 tan -1 y = sin -1 ( 2x / ( 1 + x2 )), | x | ≤ 1
2 tan-1 y = cos-1 (( 1- y2)/(1+ y2)), y ≥ 0
2 tan-1 = tan-1( 2y / (1-y2 )), -1 < y < 1
3sin-1 y = sin-1 ( 3x - 4y3)
3cos-1 y = cos-1 ( 4y3 -3y )
3tan-1 y = tan-1(( 3y - y3 ) / (1 - 3y2))
Check out the section upstairs to understand these formulas better.
