Answer:
[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
For any angle [tex]\theta[/tex], we have that:
[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]
Quadrant:
[tex]0 \leq \theta \leq \frac{\pi}{2}[/tex] means that [tex]\theta[/tex] is in the first quadrant. This means that both the sine and the cosine have positive values.
Find the cosine:
[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]
[tex](\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1[/tex]
[tex]\frac{1}{16} + (\cos{\theta})^{2} = 1[/tex]
[tex](\cos{\theta})^{2} = 1 - \frac{1}{16}[/tex]
[tex](\cos{\theta})^{2} = \frac{16-1}{16}[/tex]
[tex](\cos{\theta})^{2} = \frac{15}{16}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{15}{16}}[/tex]
Since the angle is in the first quadrant, the cosine is positive.
[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]
Answer:
b.[tex]\frac{\sqrt{15} }{4}[/tex]
Step-by-step explanation:
