Pre Calc Question

Question

Use the function value and constraint below to evaluate the given trigonometric function.

Function Value ConstraintEvaluate:

 

Answer 1

Hi,

As you know sec a = 1/cosa ----> -8 = 1/ cos a ------> cos a = -1/8 and we know tan a < 0 so the angle a is in II quadrant

cos a = -1/8 = adj / hyp ----> adj = 1 hyp = 8 also we know adj^2 + opp^2 = Hyp^2

1 + opp^2 = 64

opp^2 = 63 ----> opp = √ 63

sin a = √63 / 8 we know sin a = opp / hyp here is positive because sin in II quadrant is positive

cot a = cos a / sin a ----> cot a = (-1/8) / (√63 / 8) = -1/√63 we know 63 = 9 *7 √ 9*7 = 3√7

cot a = -1/ 3√7 = -√7 / 21

I hope it is useful,

Minoo

Answer 2

Because secθ = - 8 < 0 and tanθ < 0 by condition then θ in quadrant II.

From Pythagorian Identity tan²θ + 1 = sec²θ, tan²θ = sec²θ - 1 = (-8)² - 1 = 64 - 1= 63; tanθ = - sqrt63 = -3sqrt7. From here cotθ - 1/(3sqrt7)