Use an Identity to Write the Expression as a Single $\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }$

question 281

Multiple Choice

Use an identity to write the expression as a single trigonometric function or as a single number.
-Use the exact value $\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }$ and identities to find the exact value of $\sin 72 ^ { \circ }$ .

• A) \(\frac { ( \sqrt { 10 - 2 \sqrt { 5 } } ) ( 5 + 3 \sqrt { 5 } ) } { 40 }\)
• B) \(\frac { ( \sqrt { 10 - 2 \sqrt { 5 } } ) ( \sqrt { 5 } - 1 ) } { 4 }\)
• C) \(\frac { \sqrt { 10 + 2 \sqrt { 5 } } } { 4 }\)
• D) \(\frac { \sqrt { 10 + \sqrt { 5 } } } { 8 }\)

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Definitions:

Curvilinear Regression

A type of regression analysis used in statistics to model the complex relationship between a dependent variable and one or more independent variables when the relationship is not linear.

Independent Variable

A variable that is manipulated or controlled in an experiment to test its effect on a dependent variable, helping researchers understand cause-and-effect relationships.

Forecasting

The act of making educated guesses about future occurrences based on patterns, trends, and data analysis.

Curvilinear Relationship

A relationship between two variables where the change in one variable does not consistently result in a proportional change in the other, often depicted as a curved graph.