Inverse Trigonometric Functions 4 7 The Inverse Sine
- Slides: 20
Inverse Trigonometric Functions 4. 7
The Inverse Sine Function The inverse sine function, denoted by sin-1, is the inverse of the restricted sine function y = sin x, - /2 < x < / 2. Thus, y = sin-1 x means sin y = x, where - /2 < y < /2 and – 1 < x < 1. We read y = sin-1 x as “ y equals the inverse sine at x. ” y y = sin x - /2 < x < /2 1 - /2 -1 x Domain: [- /2, /2] Range: [-1, 1]
Finding Exact Values of -1 sin x • Let = sin-1 x. • Rewrite step 1 as sin = x. • Use the exact values in the table to find the value of in [- /2 , /2] that satisfies sin = x.
Example • Find the exact value of sin-1(1/2)
Example • Find the exact value of sin-1(-1/2)
The Inverse Cosine Function The inverse cosine function, denoted by cos-1, is the inverse of the restricted cosine function y = cos x, 0 < x < . Thus, y = cos-1 x means cos y = x, where 0 < y < and – 1 < x < 1.
Text Example Find the exact value of cos-1 (- 3 /2)
Text Example Find the exact value of cos-1 ( 2 /2)
The Inverse Tangent Function The inverse tangent function, denoted by tan -1, is the inverse of the restricted tangent function y = tan x, - /2 < x < /2. Thus, y = tan-1 x means tan y = x, where - /2 < y < /2 and – < x < .
Text Example Find the exact value of tan-1 (-1)
Text Example Find the exact value of tan-1 ( 3)
Inverse Properties The Sine Function and Its Inverse sin (sin-1 x) = x for every x in the interval [-1, 1]. sin-1(sin x) = x for every x in the interval [- /2, /2]. The Cosine Function and Its Inverse cos (cos-1 x) = x for every x in the interval [-1, 1]. cos-1(cos x) = x for every x in the interval [0, ]. The Tangent Function and Its Inverse tan (tan-1 x) = x for every real number x tan-1(tan x) = x for every x in the interval (- /2, /2).
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Using you Calculator Find the angle in radians to the nearest thousandth. Then find the angle in degree.
Example • The following formula gives the viewing angle θ, in radians, for a camera whose lens is x millimeters wide. Find the viewing angle in radians and degrees for a 28 millimeter lens.
- Inverse circular functions and trigonometric equations
- Summary of inverse trigonometric functions
- 4-6 practice inverse trigonometric functions
- Exponential rule integral
- Inverse trigonometry range and domain
- Trig differentiation
- Properties of inverse trig functions
- Integration of inverse trigonometric functions
- Laplace transform
- Cot trig ratio
- Lex stricta
- Nulla poena sine lege
- Injuria sine damno and damnum sine injuria difference
- What quadrants can inverse cosine be in
- Hyperbolic functions derivatives
- Sin^-1(4/7)
- Range of inverse sine function
- Make cos c the subject of the formula
- Trig ratios
- 4-5 practice graphing other trigonometric functions
- Six trigonometric functions of special angles