Suppose That $A B C$ Is a Right Triangle With $\angle C = 90 ^ { \circ }$

question 25

Multiple Choice

Suppose that $A B C$ is a right triangle with $\angle C = 90 ^ { \circ }$ . If $A C = 12$ and $B C = 6$ , find the quantities. $\cos A , \sin A , \tan A , \sec B , \csc B , \cot B$ .

• A) \(\cos A = \frac { 2 \sqrt { 5 } } { 5 }\) , \(\sec B = 5\) , \(\tan A = \frac { 1 } { 2 }\) , \(\sin A = \frac { \sqrt { 5 } } { 5 }\) , \(\csc B = \frac { 1 } { 5 }\) , \(\cot B = \frac { 1 } { 2 }\)
• B) \(\cos A = \frac { 2 \sqrt { 5 } } { 5 }\) , \(\sec B = \sqrt { 5 }\) , \(\tan A = 2\) , \(\sin A = \frac { \sqrt { 5 } } { 5 }\) , \(\csc B = \frac { \sqrt { 5 } } { 2 }\) , \(\cot B = \frac { 1 } { 2 }\)
• C) \(\cos A = \frac { 2 \sqrt { 5 } } { 5 }\) , \(\sec B = \frac { \sqrt { 5 } } { 2 }\) , \(\tan A = \frac { 1 } { 2 }\) , \(\sin A = \frac { \sqrt { 5 } } { 5 }\) , \(\csc B = \sqrt { 5 }\) , \(\cot B = 2\)
• D) \(\cos A = \frac { 2 \sqrt { 5 } } { 5 }\) , \(\sec B = \sqrt { 5 }\) , \(\tan A = \frac { 1 } { 2 }\) , \(\sin A = \frac { \sqrt { 5 } } { 5 }\) , \(\csc B = \frac { \sqrt { 5 } } { 2 }\) , \(\cot B = \frac { 1 } { 2 }\)
• E) \(\cos A = \frac { 2 \sqrt { 5 } } { 5 }\) , \(\sec B = \sqrt { 5 }\) , \(\tan A = \frac { 1 } { 2 }\) , \(\sin A = \frac { \sqrt { 5 } } { 5 }\) , \(\csc B = \frac { \sqrt { 5 } } { 2 }\) , \(\cot B = 2\)

Understand the significance of hydrothermal vents in the chemical evolution of life on Earth.

Grasp the basic principles of molecular self-organization and its role in the formation of cellular structures.

Recognize the importance of catalysts in the early history of life and modern cellular metabolism.

Comprehend the central role of RNA in the origin and evolution of life.

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Definitions:

Precise Predictions

Specific forecasts made about the outcomes of scientific experiments or observations.

Stimulus-Response Models

A framework in behavioral psychology where a specific stimulus leads to a particular response, emphasizing the predictable link between stimuli and reactions.

Expectancy-Value Theory

A psychological theory that explains how the motivation to engage in a behavior is influenced by the individual's expectation of success and the value they place on the success.

Motivated Behaviors

Actions that are initiated, guided, and maintained to fulfill a need or to achieve a particular goal.