# The two trigonometric functions defined for all real numbers are the_________ function and the_______ function. The domain of each of these functions is________ .

Question
Trigonometric Functions
The two trigonometric functions defined for all real numbers are the_________ function and the_______ function. The domain of each of these functions is________ .

2021-02-14
The sine function is one of the three primary functions in trigonometry, nthe others being cosine and tan functions.
The sine x or sine theta can be defined as the ratio of the opposite side of a right triangle to its hypotenuse.
and
Cos function (or cosine function) in a triangle is the ratio of the adjacent side to that of the hypotenuse.
The cosine function is one of the three main primary trigonometric functions and it is itself the complement of sine(co+sine).
The domain of a function is the set of all possible inputs for the function.
For example:
the domain of $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}$$ is all real numbers, and the domain of $$\displaystyle{g{{\left({x}\right)}}}=\frac{{1}}{{x}}$$ is all real numbers except for x=0.
The two trigonometric functions defined for all real numbers are the sine function and the_cosine function. The domain of each of these functions is$$\displaystyle{\left(−\infty,\infty\right)}$$.

### Relevant Questions

The two trigonometric functions defined for all real numbers are the_________ function and the_______ function. The domain of each of these functions is________ .
Write the trigonometric expression $$\displaystyle{\cos{{\left({{\sin}^{{-{1}}}{x}}-{{\cos}^{{-{1}}}{y}}\right)}}}$$ as an algebraic expression (that is, without any trigonometric functions). Assume that x and y are positive and in the domain of the given inverse trigonometric function.
To further justify the Cofunction Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point.
$$\displaystyle{{\sec{{6.7}}}^{\circ},}{\cos{{e}}}{c}{83.3}^{\circ}$$
How are the inverse trigonometric functions defined?
The question asks for the exact value of the trigonometric function at the given real number:
$$\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{4}}\right)}}}$$
Sketch a right triangle corresponding to the trigonometric function of the acute angle theta. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of theta. $$\displaystyle{\cos{\theta}}=\frac{{21}}{{5}}$$
When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
When using the half-angle formulas for trigonometric functions of $$\displaystyle\frac{\alpha}{{2}}$$, I determine the sign based on the quadrant in which $$\displaystyle\alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
$$\displaystyle{\sin{{t}}}=\frac{{3}}{{4}}{\quad\text{and}\quad}{\cos{{t}}}=\frac{\sqrt{{7}}}{{4}}$$
$$\displaystyle{\cos{{u}}}=\frac{{5}}{{13}}$$ , where $$\displaystyle{0}\le{u}\le\frac{\pi}{{2}}.$$