write the function value in terms of the cofunction of a complementary angle. tan 139°18 tan 139°18 = □…

write the function value in terms of the cofunction of a complementary angle. tan 139°18 tan 139°18 = □ (□°□) (simplify your answers. type the cofunction abbreviation in the first input box. type th input box.)

write the function value in terms of the cofunction of a complementary angle. tan 139°18 tan 139°18 = □ (□°□) (simplify your answers. type the cofunction abbreviation in the first input box. type th input box.)

Answer

Explanation:

Step1: Use the co - function identity

The co - function identity for tangent is (\tan\theta=\cot(90^{\circ}-\theta)) when (\theta) is an acute angle. But for (\theta = 139^{\circ}18'), we know that (\tan\theta=\tan(180^{\circ}-\alpha)=-\tan\alpha) where (\alpha = 40^{\circ}42') ((180^{\circ}-139^{\circ}18'=40^{\circ}42')), and also (\tan\theta=\cot(90^{\circ}-\theta + 180^{\circ}n)).

Another way is to use the formula (\tan\theta=\cot(90^{\circ}-\theta + 180^{\circ})) (since (\tan\theta=\cot(270^{\circ}-\theta)) and also (\tan\theta =-\cot(\theta - 90^{\circ}))).

We know that (\tan\theta=\cot(90^{\circ}-\theta)) in the co - function relationship. For (\theta = 139^{\circ}18'), we can write (\tan139^{\circ}18'=\cot(139^{\circ}18'-90^{\circ}))

Step2: Calculate the angle

Calculate (139^{\circ}18'-90^{\circ}). (139^{\circ}18'-90^{\circ}=(139 - 90)^{\circ}18'=49^{\circ}18')

Answer:

(\tan139^{\circ}18'=\cot(49^{\circ}18'))