Find tan if cos = 1/2 and sin<0 can you explain step by step

Question

I don’t kn how to use the identity in here can u help me

Answer 1

cos x = 1/2 and sin x < 0. That means that cos x > 0 and sin x < 0, which means that cos x is positive and sin x is negative. To find the quadrant which this happens, I need to use the ASTC (All students take calculus) (All Sin Tan Cos) rule. In Quadrant 1, ALL three trig functions (sin, cos, tan are positive), in Quadrant 2, only sin is positive, which means that cos and tan is negative. In Quadrant 3, only tan is positive, which means that cos and sin are negative, and in Quadrant 4, cos is positive, which means that sin and tan are negative. I'm looking at quadrant 4, since cos is positive and sin is negative. Go to quadrant 4, remember your trig ratios, and you'll get that when cos x = 1/2, x = 60 degrees or 2pi/3 radians. However, since you're in quad 4, remember your reference angles, and you will get that x = 300 degrees or 5pi/3 radians. hope this helps!