Let $P ( x , y )$ Denote the Point Where the Terminal Side of Angle

question 5

Multiple Choice

Let $P ( x , y )$ denote the point where the terminal side of angle $\theta$ (in standard position) meets the unit circle. Use the information to evaluate the six trigonometric functions of $\theta$ . $P$ is in Quadrant IV and $y = - \frac { 3 } { 4 }$ .

• A) \(\sin \theta = - \frac { \sqrt { 7 } } { 4 }\) , \(\cos \theta = \frac { 3 } { 4 }\) , \(\tan \theta = - \frac { \sqrt { 7 } } { 3 }\) , \(\sec \theta = \frac { 4 } { 3 }\) , \(\csc \theta = \frac { 4 \sqrt { 7 } } { 7 }\) , \(\cot \theta = \frac { 3 \sqrt { 7 } } { 7 }\)
• B) \(\sin \theta = - \frac { \sqrt { 7 } } { 4 }\) , \(\cos \theta = \frac { 3 } { 4 }\) , \(\tan \theta = \frac { \sqrt { 7 } } { 3 }\) , \(\sec \theta = \frac { 4 } { 3 }\) , \(\csc \theta = - \frac { 4 \sqrt { 7 } } { 7 }\) , \(\cot \theta = \frac { 3 \sqrt { 7 } } { 7 }\)
• C) \(\sin \theta = - \frac { 3 } { 4 }\) , \(\cos \theta = \frac { \sqrt { 7 } } { 4 }\) , \(\tan \theta = - \frac { 3 \sqrt { 7 } } { 7 }\) , \(\sec \theta = \frac { 4 \sqrt { 7 } } { 7 }\) , \(\csc \theta = - \frac { 4 } { 3 }\) , \(\cot \theta = - \frac { \sqrt { 7 } } { 3 }\)
• D) \(\sin \theta = \frac { \sqrt { 7 } } { 4 } \quad \cos \theta = - \frac { 3 } { 4 } \quad \tan \theta = - \frac { \sqrt { 7 } } { 3 }\) \(\sec \theta = \frac { 4 } { 3 }\) , \(\csc \theta = \frac { \sqrt { 7 } } { 7 }\) , \(\cot \theta = - \frac { \sqrt { 7 } } { 7 }\)
• E) \(\sin \theta = \frac { 3 } { 4 }\) , \(\cos \theta = - \frac { \sqrt { 7 } } { 4 }\) , \(\tan \theta = \frac { 3 \sqrt { 7 } } { 7 }\) , \(\sec \theta = - \frac { 4 \sqrt { 7 } } { 7 }\) , \(\csc \theta = \frac { 4 } { 3 }\) , \(\cot \theta = \frac { \sqrt { 7 } } { 3 }\)

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Definitions:

Neurotransmitter System

A complex network of neurons communicating through chemical messengers known as neurotransmitters to modulate various physical and psychological functions.

Dopamine

A chemical messenger that plays a critical role in controlling body movement, focus, memory, motivation, and the reward system.

GABA

Gamma-Aminobutyric Acid, a neurotransmitter in the brain that inhibits or reduces activity of neurons.

Serotonin

A neurotransmitter involved in the regulation of mood, appetite, and sleep, and has some cognitive functions, including memory and learning.