Explain why the domain of the sine function must be restricted in order to define its inverse function.

Q: What is the fundamental identity for hyperbolic functions?

A: Hyperbolic functions have identities that are similar to the identities for trigonometric functions…

Q: Sine, cosine, and tangent have two quadrants that are more important than the others. It is…

A: Explanation of the answer is as follows

Q: When is the arcsin function also a square root function

A:

Q: Can the sin x ever be a value greater than 1?

A: We have to find the sinx value

Q: Use double- and half-angle formulas to find the exact value of the expression sin 22.5°.

A: Given: sin 22.5° To find: The exact value by using double and half-angle formula.

Q: ASK YOUR TEACHER The length of each of the two equal sides of an isosceles triangle is 26 meters…

A: Step 1: Draw the perpendicular from the vertex to the base.The perpendicular AD bisects the angle…

Q: 2. Describe the transformations (in point form) required to transform the function y= cos x to the…

A: The solution are next step

Q: -co e-tsint (1) Evaluate f tsint dt t

A: Given integral is ∫0∞e-tsinttdt. Evaluate the integral ∫0∞e-tsinttdt.

Q: Write sin(3x) cos(7x) as a sum of trigonometric functions.

A: Given trigonometric function is  sin3x cos7x. Write the sin3x cos7x as a sum of trigonometric…

Q: During a 12.8-hour period, the water level at Bay of Fundy, Nova Scotia, started at mean sea level…

A: We have to find model function which satisfies all given data.

Q: A Ferris wheel is built in such a way that the height h (in feet) a seat on the wheel is above is…

A: It is given that Ferris wheel is built in such a way that the height h (in feet) a seat on the wheel…

Q: Simplify  1/cos a 1/sin b

A: we know that  1cosθ=secθ1sinθ=cosecθ

Q: Match the following inverse functions with its corresponding value in radians. Please take note of…

A: 1) arccos ( -12 )cos-1( -12 )

Q: The height above the ground of a rider on a Ferris wheel can be modelled by the sinusoidal function…

A: To find the maximum height of the rider above the ground based on the sinusoidal function, we need…

Q: 33

A: Consider the inverse functions Determine the reflection line.

Q: Which inverse trigonometric function has a range of 0 < y < π?

A: To find which inverse trigonometric function has a range of 0<y<π, that is the interval 0,π…

Q: Question 2 (a). Let v(0) = sin(0), where is in radians. Graph v(0). Label intercepts, maximum…

A: Given function is (a) Noted that In other words , maximum values of  is  and attained minimum values…

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.