One of Sin X, Cos X, and Tan X Is $\sin x = - \frac { 1 } { 5 } , \quad x$

question 398

Multiple Choice

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
- $\sin x = - \frac { 1 } { 5 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

• A) \(\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }\)
• B) \(\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }\)
• C) \(\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }\)
• D) \(\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }\)

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Definitions:

P-Value

The probability of observing test results at least as extreme as the results actually observed, assuming that the null hypothesis is true.

West Nile Virus

A virus transmitted to humans and animals through the bite of an infected mosquito, known for causing West Nile fever.

Null Hypothesis

A hypothesis that there is no effect or no difference, and it serves as a default hypothesis in statistical hypothesis testing.

Alternative Hypothesis

A statement that suggests there is a statistically significant difference between two or more data sets, contrary to the null hypothesis.