MATH SOLVE

3 months ago

Q:
# The terminal side of angle theta in standard position passes through the point (8/17, 15/17)on the unit circle.Find cos thetaSin thetaTan theta Sec thetaCot thetaCsc theta

Accepted Solution

A:

Answer:cos Ф = 8/17sin Ф = 15/17tan Ф = 15/8sec Ф = 17/8csc Ф = 17/15cot Ф = 8/15Step-by-step explanation:Draw the triangle in the first quadrantbase = 8/17 and Perpendicular = 15/17Calculate the hypotenuse using Pythagoras theorem(h)^2 = (b)^2 + (p)^2(h)^2 = (8/17)^2 + (15/17)^2 (h)^2 = 64/289 + 225/289(h)^2 = 289/289h = 1So, Base = 8/17, Perpendicular = 15/17 and Hypotenuse = 1Now finding sin Ф = Perpendicular / Hypotenusesin Ф = 15/17/1sin Ф = 15/17cos Ф = Base / Hypotenusecos Ф = 8/17/1cos Ф = 8/17tan Ф = sin Ф/cos Фtan Ф = 15/17 ÷ 8/17tan Ф = 15/17 * 17/8tan Ф = 15/8sec Ф = 1/cos Фcos Ф = 8/17sec Ф = 17/8csc Ф = 1/sin Фsin Ф = 15/17csc Ф = 17/15cot Ф = 1/tan Фtan Ф = 15/8cot Ф = 8/15