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# How are the inverse trigonometric functions defined?

Question
Trigonometric Functions
asked 2020-11-05
How are the inverse trigonometric functions defined?

## Answers (1)

2020-11-06
To write how the inverse trigonometric functions are defined?
The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant function.
The inverse trigonometric function are defined as the inverse of basic trigonometric functions and it is denoted by $$\displaystyle{{\sin}^{ ### Relevant Questions asked 2020-11-26 Write the trigonometric expression \(\displaystyle{\cos{{\left({{\sin}^{{-{1}}}{x}}-{{\cos}^{{-{1}}}{y}}\right)}}}$$ as an algebraic expression (that is, without any trigonometric functions). Assume that x and y are positive and in the domain of the given inverse trigonometric function.
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The two trigonometric functions defined for all real numbers are the_________ function and the_______ function. The domain of each of these functions is________ .
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To further justify the Cofunction Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point.
$$\displaystyle{{\sec{{6.7}}}^{\circ},}{\cos{{e}}}{c}{83.3}^{\circ}$$
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When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
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When using the half-angle formulas for trigonometric functions of $$\displaystyle\frac{\alpha}{{2}}$$, I determine the sign based on the quadrant in which $$\displaystyle\alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
asked 2021-03-06
Given the values for sin t and cos t, use reciprocal and quotient identities to find the values of the other trigonometric functions of t.
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The trigonometric functions $$\displaystyle{\sec{{\left({135}^{\circ}\right)}}}$$
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sec theta = -3, tan theta > 0ZSK. Find the exact value of the remaining trigonometric functions of
thetaZSK.
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