Trigonometry: The basic MATLAB trigonometric functions are sin, cos, tan, cot, sec, and csc. The inverses, e.g., arcsin, arctan, etc., are cal- culated with asin, atan, etc. The same is true for hyperbolic functions. The inverse function at an2 takes two arguments, y and z, and gives the four- quadrant inverse tangent. The argument of these functions must be in radians. Calculate the following quantities: • sin, cos 7, and tan . • sin²+ cos² (Typing sin^2(x) for sin²r will produce an error). y = cosh²z-sinh²z, with z = 32m.

The unit circle and trigonometric functions go hand-in-hand. Each angle on the unit circle creates a point for a trigonometric function using the angle and function-related point value. First we will look at the sine curve and how it can be graphed using the unit circle. We have learned that sin t = y. This means that for each angle, the y-value of its related point is the y- coordinate in a point on the graph of f(x) = sin x. For example, the point associated with the angle, %3D is 6' %3D - G). So, f () = sin" = Therefore, the related point on the graph of f(x) = sin x is (",). %D 6. Let's try a few... 0 = 0: The point associated with the angle, 0 radians, is (1,0). So, f(0) = sin 0 = 0. Therefore, the point associated with the angle, 0, is (0,0). %3D

Find the exact value of the following trigonometric function using the unit circle. tan - 57 tan (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Use the periodic properties of the trigonometric functions to simplify each expression to a single function of θ.   Cos(θ+2) x csc(θ +2pi)=