Question

If cosine of x equals 1 / 2, what is sin(x) and tan(x)? Explain your steps in complete sentences.

Answer 1

Answer:

Step-by-step explanation:

+ we have

[sin(x)]^2 + [cos(x)]^2 = 1

so [cos(x)]= 1- [sin(x)]^2 = 1- (1/2)^2 = 1- 1/4 = 3/4

Then cos(x) can take one of two values;

+ cos(x) =$\frac{\sqrt{3} }{2}$

then tan(x)= sin(x)/cos(x) = (1/2)/ ($\frac{\sqrt{3} }{2}$) = $\frac{\sqrt{3} }{3}$

+ cos(x) = - $\frac{\sqrt{3} }{2}$

then tan(x)= sin(x)/cos(x) = (1/2)/ (- $\frac{\sqrt{3} }{2}$) = - $\frac{\sqrt{3} }{3}$

Have a good day