SOLUTION: Find the values of all six trigonometric functions for an angle in standard position having each point on its terminal side. Questions: (-8,15) (3, -4) and (-2squarerootof2, 2s

Algebra ->  Trigonometry-basics -> SOLUTION: Find the values of all six trigonometric functions for an angle in standard position having each point on its terminal side. Questions: (-8,15) (3, -4) and (-2squarerootof2, 2s      Log On


   

Question 551164: Find the values of all six trigonometric functions for an angle in standard position having each point on its terminal side.
Questions:
(-8,15)
(3, -4)
and (-2squarerootof2, 2squarerootof2)
I know I need to find sin, cosine, tangent and their reciprocals. That's all I got to....
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the point (-2sqrt%282%29,sqrt%282%29)


 

Draw a perpendicular to the x-axis. That makes a right triangle.  Label the
horizontal side x = the x-coordinate of the point = -2sqrt(2), and the vertical
side y = the y-coordinate of the point sqrt(2)).


 

Calculate the hypotenuse of the right triangle using the Pythagorean
theorem:

r² = x² + y²
r² = (-2sqrt%282%29)² + (%28sqrt%282%29%29%5E2)²
r² = (-2)²(sqrt%282%29)² + 2
r² = 4(2) + 2
r² = 8 + 2
r² = 10
r = sqrt%2810%29

Label r:



sin%28theta%29 = y%2Fr = sqrt%282%29%2Fsqrt%2810%29 = sqrt%282%29%2Fsqrt%2810%29·%28sqrt%2810%29%29%2Fsqrt%2810%29 = sqrt%2820%29%2F10 = sqrt%284%2A5%29%2F10 = 2sqrt%285%29%2F10 = sqrt%285%29%2F5 

cos%28theta%29 = x%2Fr = %28-2sqrt%282%29%29%2Fsqrt%2810%29 = %28-2sqrt%282%29%29%2Fsqrt%2810%29·%28sqrt%2810%29%29%2Fsqrt%2810%29 = %28-2sqrt%2820%29%29%2F10 = %28-2sqrt%284%2A5%29%29%2F10 = %28-2%2A2sqrt%285%29%29%2F10 = %28-4sqrt%285%29%29%2F10 = -2sqrt%285%29%2F5

tan%28theta%29 = y%2Fx = %28sqrt%282%29%29%2F%28-2sqrt%282%29%29 = -%28sqrt%282%29%29%2F2sqrt%282%29 =  -%28cross%28sqrt%282%29%29%29%2F2cross%28sqrt%282%29%29 = -1%2F2

sec%28theta%29 = r%2Fx = sqrt%2810%29%2F%28-2sqrt%282%29%29 = sqrt%2810%29%2F%28-2sqrt%282%29%29·%28sqrt%282%29%29%2Fsqrt%282%29 = %28sqrt%2820%29%29%2F%28-2%2A2%29 = %28-sqrt%284%2A5%29%29%2F4 = %28-2sqrt%285%29%29%2F4 = -sqrt%285%29%2F2

csc%28theta%29 = r%2Fy = sqrt%2810%29%2F%28sqrt%282%29%29 = sqrt%2810%2F2%29 = sqrt%285%29

cot%28theta%29 = x%2Fy = %28-2sqrt%282%29%29%2F%28sqrt%282%29%29 = %28-2cross%28sqrt%282%29%29%29%2Fcross%28sqrt%282%29%29 = -2


Edwin