What is the value of tan 570°

Solution

To find tan 570º , we reduce the angle by subtracting multiples of 360º until we get an equivalent angle between 0º and 360º. 570º - 360º = 210º Therefore, tan(570º) = tan(210º) Now, tan(210º) = tan(180º + 30º) Using the formula tan(180º + θ) = tan(θ) , we get: tan(210º) = tan(30º) And we know: tan(30º) = 1/√3 However, since 210º is in the third quadrant where tan is positive, we have: tan(210º) = tan(30º) = 1 / √ 3 Therefore, the value of tan(570º) is 1 / √ 3  .