Indicate the quadrant(s) in which the terminal side of $$ \theta $$ could lie if: $$ \begin{array}{c}\cos (\theta)=\frac{\sqrt{3}}{2} \text {. } \ \text { Select all that apply. } \ \square \text { quadrant I } \ \square \text { quadrant II } \ \square \text { quadrant III } \ \text { quadrant IV }\end{array} $$

Question

UpStudy AI · Accepted Answer

To determine the quadrants in which the terminal side of $$ 	heta $$ could lie given that $$ \cos(	heta) = \frac{\sqrt{3}}{2} $$, we can analyze the properties of the cosine function.

1. **Understanding Cosine Values:**
   - The cosine function is positive in the first and fourth quadrants.
   - In the first quadrant (Quadrant I), both sine and cosine are positive.
   - In the fourth quadrant (Quadrant IV), sine is negative and cosine is positive.

2. **Finding the Reference Angle:**
   - The reference angle for $$ \cos(	heta) = \frac{\sqrt{3}}{2} $$ corresponds to $$ 	heta = 30^\circ $$ or $$ 	heta = \frac{\pi}{6} $$ radians.

3. **Determining Possible Quadrants:**
   - Since cosine is positive, $$ 	heta $$ can be in:
     - Quadrant I (where $$ 	heta = 30^\circ $$)
     - Quadrant IV (where $$ 	heta = 360^\circ - 30^\circ = 330^\circ $$)

Based on this analysis, the terminal side of $$ 	heta $$ could lie in:

- **Quadrant I**
- **Quadrant IV**

Thus, the correct selections are:
- [x] Quadrant I
- [ ] Quadrant II
- [ ] Quadrant III
- [x] Quadrant IV
The terminal side of $$ 	heta $$ could lie in **Quadrant I** and **Quadrant IV**.

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Trigonometry Questions