Question

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

Column I: 1.
csc⁻¹ 4
Column II:
A. 88.09084757°
B. 63.25631605°
C. 1.909152433°
D. 17.45760312°
E. 0.2867453858
F. 1.962610506
G. 14.47751219°
H. 1.015426612
I. 1.051462224
J. 0.9925461516

Accepted Answer

Identify the trigonometric functions or inverse functions given in Column I. For example, recognize that csc⁻¹ 4 means the inverse cosecant of 4, which is the angle whose cosecant is 4. Recall the definitions and ranges of the inverse trigonometric functions involved. For instance, the inverse cosecant function, csc⁻¹ x, returns an angle $$ 	heta $$ such that $$ \csc 	heta = x $$, and typically $$ 	heta $$ lies in specific intervals depending on the function's principal values. Calculate or estimate the angle values for each inverse trigonometric function using a calculator or known identities. For example, to find $$ 	heta = \csc^{-1} 4 $$, use the relationship $$ \csc 	heta = 4 $$ which implies $$ \sin 	heta = \frac{1}{4} $$, then find $$ 	heta = \sin^{-1} \left( \frac{1}{4} ight) . $$Match each calculated angle or function value with the closest approximation listed in Column II by comparing the numerical values. Pay attention to whether the values are in degrees or radians and convert if necessary. Verify the matches by checking the consistency of the values with the properties of the trigonometric functions, ensuring that the approximations correspond correctly to the given functions or angles.

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Key Concepts

Inverse Trigonometric Functions

Trigonometric Function Values and Angle Approximations

Domain and Range of Trigonometric Functions