Tutor profile: Syeda A.

Find the value of 3 primary trig ratios when cos (a) = -4/5 and the angle a is not in 3rd Quadrant

First of all find the quadrant, since cosine value is negative and we know (by CAST rule) cosine is negative in 2nd and 3rd quad but here it is mentioned that the angle is not in 3rd quadrant which clearly means that the angle is in 2nd Quadrant. Now cos (a) = -4/5, we also that cos (a) = adjacent/hypotenuse such that, cos (a) = -4/5 = adj/hyp => -4 is adj and 5 is hyp now using Pythagorean Theorem we find the value for opposite (opp) Opp^2 = Hyp^2 - adj^2 Opp^2 = (5^2) - (-4)^2 Opp^2 = 9 Opp = 3 now for sin(a) = opp/hyp sin(a) = 3/5 (we are working in 2nd Quadrant where sine is positive) tan(a) = opp/adj = 3/(-4) tan(a) = -3/4

Evaluate the derivative of 5x^6

By the power rule: d/dx (5x^6) = 5*6(x^6-1) = 30x^5 d/dx (5x^6) = 30x^5

Find the value of "b": 2(a -3) + 4b - 2(a -b -3) = -5

Given algebraic expression 2 (a -3) + 4 b - 2 (a - b - 3) + 5 = 0 Multiply factors. 2 a - 6 + 4 b - 2 a + 2 b + 6 + 5 = 0 Group like terms. 6 b + 5 = 0 6b = -5 b = -5/6