Answer:
b
Step-by-step explanation:
Using the trigonometric identity
• sin²x + cos²x = 1 , hence
cosx = ± [tex]\sqrt{1-sin^2x}[/tex]
cosΦ > 0 for 0 < Φ < [tex]\frac{\pi }{2}[/tex]
cosΦ = [tex]\sqrt{1-(\frac{1}{4})^2 }[/tex] = [tex]\sqrt{1-\frac{1}{16} }[/tex] = [tex]\sqrt{\frac{15}{16} }[/tex] = [tex]\frac{\sqrt{15} }{4}[/tex] → b
Answer:
Choice b is correct answer.
Step-by-step explanation:
We have to find the value of cos∅x where the value of sin∅ is given.
Given that
sin∅ = 1/4
We use trigonometric identity to solve this question.
Trigonometric identity:
sin²∅+cos²∅=1
Separating cos²∅
cos²∅= 1-sin²∅
Taking square root to above equation
cos∅=√1-sin²∅
cos∅=√1-(sin∅)²
Putting the given value of sin∅,we get
cos∅= √1-(1/4)²
cos∅= √1-1/16
cos∅=√16-1/16
cos∅= √15/16
cos∅= (√15)/4
Hence, the answer is Choice b.
