Homework SourseUse the figure to find the exact value of the trigonometric
Use the figure to find the exact value of the trigonometric functions. 15 8 sing = csc- 2 2 tan = COS 2 ![Use the figure to find the exact value of the trigonometric functions. 15 8 sing = csc- 2 2 tan = COS 2 SolutionP = 15 B = 8 H = sqrt[P^2 + B^2] = 17 = arctan(](/WebImages/33/use-the-figure-to-find-the-exact-value-of-the-trigonometric-1097438-1761579093-0.webp "Use the figure to find the exact value of the trigonometric functions. 15 8 sing = csc- 2 2 tan = COS 2 SolutionP = 15 B = 8 H = sqrt[P^2 + B^2] = 17 = arctan(")
Solution
P = 15
B = 8
H = sqrt[P^2 + B^2] = 17
= arctan(15/8) = 61.93 degree (First quadrant)
sin = P/H = 15/17
cos = B/H = 8/17
tan = P/B = 15/8
Now
cos = 2*cos2(/2) – 1
cos(/2) = sqrt[(cos + 1)/2] = sqrt[(8/17 + 1)/2] = sqrt(25/34) = 5/34
sin(/2) = sqrt[(1 – cos)/2] = sqrt[(1 – 8/17)/2] = sqrt(9/34) = 3/34
tan(/2) = sin(/2)/cos(/2) = 3/5
csc(/2) = 1/sin(/2) = 34/3
sec(/2) = 1/cos(/2) = 34/5
cot(/2) = 1/tan(/2) = 5/3
