# 4cos^2x−3=0

Question
Trigonometric Functions
$$\displaystyle{4}{{\cos}^{{2}}{x}}−{3}={0}$$

2021-03-07
$$\displaystyle{4}{\left({\cos}^{{2}}\right)}{x}-{3}={0}$$
$$\displaystyle{4}{\left({\cos}^{{2}}\right)}={3}$$
$$\displaystyle{\left({\cos}^{{2}}\right)}{x}=\frac{{3}}{{4}}$$
$$\displaystyle{\cos{{x}}}=\frac{{\sqrt{{3}}}}{{2}}$$
$$\displaystyle{x}={{\cos}^{{-{{1}}}}{\left(\frac{{\sqrt{{3}}}}{{2}}\right)}}$$
x=30

### Relevant Questions

Which statement cannot be true? Explain.
A. $$\displaystyle{\sin{{A}}}={0.5}$$
B. $$\displaystyle{\sin{{A}}}={1.2654}$$
C. $$\displaystyle{\sin{{A}}}={0.9962}$$
D. PSKsin A = 3/4
Let theta be an angle in standard position, $$\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0}$$. Name the quadrant in which theta lies.
Given the following information about one trigonometric function, evaluate the other five functions.
$$\displaystyle{\cos{{u}}}=\frac{{5}}{{13}}$$ , where $$\displaystyle{0}\le{u}\le\frac{\pi}{{2}}.$$
Find the values of the other trigonometric functions of theta if $$\displaystyle{\cot{\theta}}=-\frac{{4}}{{3}}{\quad\text{and}\quad}{\sin{\theta}}{<}{0}$$.
If $$f(\theta) = \sin \theta = 0.2$$
Find $$f(\theta + \pi)$$
$$y=\sin(\pi x)$$
When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
Find derivative of trigonometric function $$y=(3(1-sin x))/(2cos x)$$
The provided text passage contains a trigonometric equation and its solution, followed by a set of relevant questions. The main content is the step-by-step solution to the equation \(4\cos^2(x) - 3 = 0\).
single_question_with_answer

the passage starts with the equation \(4\cos^2(x) - 3 = 0\) and proceeds to solve it, providing the final answer \(x = 30^\circ\). therefore, it contains a single mathematical question with a provided answer.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 4cos^2x−3=0

Question
Trigonometric Functions
$$\displaystyle{4}{{\cos}^{{2}}{x}}−{3}={0}$$

2021-03-07
$$\displaystyle{4}{\left({\cos}^{{2}}\right)}{x}-{3}={0}$$
$$\displaystyle{4}{\left({\cos}^{{2}}\right)}={3}$$
$$\displaystyle{\left({\cos}^{{2}}\right)}{x}=\frac{{3}}{{4}}$$
$$\displaystyle{\cos{{x}}}=\frac{{\sqrt{{3}}}}{{2}}$$
$$\displaystyle{x}={{\cos}^{{-{{1}}}}{\left(\frac{{\sqrt{{3}}}}{{2}}\right)}}$$
x=30

### Relevant Questions

Which statement cannot be true? Explain.
A. $$\displaystyle{\sin{{A}}}={0.5}$$
B. $$\displaystyle{\sin{{A}}}={1.2654}$$
C. $$\displaystyle{\sin{{A}}}={0.9962}$$
D. PSKsin A = 3/4
Let theta be an angle in standard position, $$\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0}$$. Name the quadrant in which theta lies.
Given the following information about one trigonometric function, evaluate the other five functions.
$$\displaystyle{\cos{{u}}}=\frac{{5}}{{13}}$$ , where $$\displaystyle{0}\le{u}\le\frac{\pi}{{2}}.$$
Find the values of the other trigonometric functions of theta if $$\displaystyle{\cot{\theta}}=-\frac{{4}}{{3}}{\quad\text{and}\quad}{\sin{\theta}}{<}{0}$$.
If $$f(\theta) = \sin \theta = 0.2$$
Find $$f(\theta + \pi)$$
$$y=\sin(\pi x)$$
When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
Find derivative of trigonometric function $$y=(3(1-sin x))/(2cos x)$$
user
The provided text passage contains a trigonometric equation and its solution, followed by a set of relevant questions. The main content is the step-by-step solution to the equation \(4\cos^2(x) - 3 = 0\).

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage starts with the equation \(4\cos^2(x) - 3 = 0\) and proceeds to solve it, providing the final answer \(x = 30^\circ\). Therefore, it contains a single mathematical question with a provided answer.