Trigonometry Answers

Solve each triangle. Round answer to nearest tenth. Triangle RPQ angle P=18 degrees angle Q= 122 degrees r=25

Jack and Jill ran up a hill to fetch a pail of water. They ran 100m to get to the top of a 30m tall hill. What is the degree of incline of the hill?

In △ ABC, ∠C = 30o

, c = 8.2cm, and b = 12.2cm.

Draw the triangle(s) and show 2 cases if there are two.

Maria says that sin A= disagree 12/18, cos A= 9/18, and tan A= 12/9. Do you agree or disagree? If you agree, explain why. If you disagree, explain what she did incorrectly and provide the correct solution.

In a circle of radius 30 inches, a central angle of 35 will intersect the circle forming an arc of length _____.

Let w be a negative real number, z a 6th root of w.

a) Show that z(k) = p^1/6 [cos ( pi + 2 * k* pi / 6) + i sin ( pi + 12 * k * pi / 6)], k = v, 1,2,3,4,5 is a formula for the 6th roots of w.

b) Hence determine 6th roots of - 729.

c) Given z = cosA + i sin A and u + iv = (1+z) (1+ z^2). Prove that v = u tan(3A/2), u^2 + v^2 = 16 cos ^2(A/2) cos^2A

(De Moivres theorem) - Use Cos5A and sin4A as polynomials in sinA and CosA to evaluate:

1) sin pi/5
2) sin2*pi/5
3) cos pi/5.

Louise is painting around a window frame on the outside of her house. Her ladder is 3.5m long and she placed it 1 m from the house. What is the vertical distance that the ladder reaches up the house? Round to one decimal place. Use the Pythagorean theorem.

Using de Moivres theorem, express

Cos5A and sin4A as polynomials in sin A and cos A.

pls i need to know the diagram of this bearing of a village R is 10km from a point P on a bearing 025° from P. Another village A is 6km from P on a bearing 162°. Calculate (a) distance of R from A. (b) bearing of R from A