One of Sin X, Cos X, and Tan X Is $\cos x = - \frac { 1 } { 3 } , \quad x$

question 178

Multiple Choice

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
- $\cos x = - \frac { 1 } { 3 } , \quad x$ in $\left[ \pi , \frac { 3 \pi } { 2 } \right]$

• A) \(\sin x = - \frac { 2 \sqrt { 2 } } { 3 } , \tan x = 2 \sqrt { 2 }\)
• B) \(\sin x = \frac { 2 \sqrt { 2 } } { 3 } , \tan x = - 2 \sqrt { 2 }\)
• C) \(\sin x = \frac { 2 \sqrt { 2 } } { 3 } , \tan x = 2 \sqrt { 2 }\)
• D) \(\sin x = - \frac { 2 \sqrt { 2 } } { 3 } , \tan x = - 2 \sqrt { 2 }\)

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Definitions:

Transcription Rate

The transcription rate refers to the speed at which genetic information is copied from DNA to RNA, affecting gene expression levels.

Enhancer

A short region of DNA that can be bound with proteins (transcription factors) to increase the likelihood that transcription of a particular gene will occur.

Lac Operon

A gene system found in E. coli and other bacteria that regulates the metabolism of lactose, demonstrating gene regulation principles.

Operon's Genes

A group of genes in prokaryotes that function together, controlled by a single regulatory signal or promoter.