Solve each equation for x.
y = 1/2 tan (3x + 2), for x ...

Question

Solve each equation for x.

y = 1/2 tan (3x + 2), for x in [-2/3 - π/6, -2/3 + π/6]

Accepted Answer

Hello, everyone. We are asked to find the exact values of the given equation Y equals 1/5 tangent of the parentheses. Seven X plus four for X in the interval between negative 4/7 minus pi divided by 14 to negative 4/7 plus pi divided by 14. Our answer choices are A X equals 1/7 open bracket. Inverse tangent of five Y closed parentheses plus four closed square bracket. BX equals seven open square bracket. Inverse tangent of five, Y minus four closed square bracket. CX equals 1/7. The inverse tangent of five Y minus four close square bracket. DX equals seven, multiplied by square bracket, inverse tangent of five Y plus four, close square bracket. OK. So that was a mouthful um starting with the equation Y equals 1/5 the tangent of seven X plus four, which is in parentheses. So when X is in that interval, it is a 1 to 1 function. So we should be able to just use algebra and a little bit of trig to solve this. So I'm gonna start by getting this 1/5 to the other side. So I'm gonna do that by multiplying both sides by five. So I get five Y equals the tangent of seven X plus four from there. I'm gonna go take the inverse tangent of both sides. So I can say the inverse tangent of five Y will equal seven X plus four. And now I'm gonna subtract four from both sides to try to isolate X. So the inverse tangent of five Y and then subtracting four from it equals seven X. And I'm gonna divide both sides by seven to get X by itself. I want to rewrite this though as 1/7 versus dividing it by seven. So I get 1/7 and then I'm opening a square bracket, putting the inverse tangent of five Y and then minus four close bracket will equal X. So this would give us our exact solutions for that interval and this is our answer. So 1/7 multiplied by the square bracket, inverse tangent of five Y minus four. And that is answer choice C have a nice day.

Struggling with Trigonometry?

Solve each equation for x.
y = 1/2 tan (3x + 2), for x in [-2/3 - π/6, -2/3 + π/6]

Watch next

Inverse Sine, Cosine, & Tangent practice set